text:
\section{Introduction}

The Survey of Income and Program Participation (SIPP) is the largest government survey of people
on public assistance in the United States. It includes longitudinal
data on income, labor force information, participation and eligibility
for governmental assistance programs, and general demographic
characteristics for individuals on public assistance; as such, it is used by a broad community of researchers and policy-makers  \citep{kinnerreiterjos}.
In 2014, the Census Bureau redesigned the SIPP to utilize a longer
reference period (twelve months, instead of four) and a new instrument
that incorporates an event  history calendar  \citep{Moore2009}. The
Census Bureau made these changes with the hope of reducing costs and
respondent burden while improving accuracy.

To evaluate the redesign,  the Census Bureau conducted a field test by giving the new survey to a non-overlapping sample of individuals drawn from the
same frame used to construct the 2008 production SIPP panel. The field test was restricted to individuals in low income strata in 20 states.
The Census  Bureau also constructed a comparison dataset from the production SIPP panel comprising individuals from the same strata and states, with the intention of
assessing whether or not the change in collection instruments resulted in different distributions of key variables. Additional details
are available in \cite{USCensus2013}.

The data from the field test suffered from item nonresponse, as did the data
from the production SIPP.  For example, among the sampled field
test individuals, approximately 16\% are missing employment status and, for those who reported participation in the Supplemental Nutrition Assistance Program (SNAP),
approximately 59\% are missing the benefit amounts.  Unless the
missing data mechanisms are identical in both datasets,
e.g., both missing completely at random \citep{Rubin1976},
comparisons of available case analyses may result in inaccurate
conclusions about where estimates from the old and new designs differ.

Given the objective of comparing two datasets on many
analyses, a sensible approach is to create and utilize
multiply-imputed versions \citep{Rubin1987} of each sample.  In
multiple imputation (MI) the imputer repeatedly samples values of the
missing data from their predictive distribution under an appropriate
 model to create $m>1$ completed datasets.  The analyst
then computes point and variance estimates in each of the $m$
datasets, and combines them using straightforward rules
\citep{Rubin1987, reiter:raghu:07}.  These rules allow the analyst to account for
uncertainty due to the missing data when making inferences.

The SIPP data have distributional features that are
challenging to capture with imputation based on
standard (semi-)parametric models.
For example, some continuous variables have different variances and skewness at
different combinations of the categorical variables, and the
categorical variables have complex dependencies.
Thus, it is desirable to use imputation models that can capture such features in
each dataset with minimal tuning.

In this article, we introduce a nonparametric Bayesian joint
model for mixed continuous and categorical data suitable for use as a
flexible, fully coherent multiple imputation engine.  The basic idea
is to
fuse two Dirichlet Process (DP) mixtures: a mixture of multinomial distributions (for the categorical data) and a mixture of multivariate normal regressions (for the continuous data, conditionally on the categorical variables).
We model dependence between the
categorical and  continuous variables by (i)
specifying the means of the normal distributions
as component-specific functions of the categorical variables, and (ii) inducing dependence in the separate component assignments via a
hierarchical model. As we illustrate, the model includes
local dependence---i.e., dependence among variables within mixture components---between the categorical and continuous data;
thus, we call it a hierarchically coupled mixture model with local
dependence (HCMM-LD). Local dependence allows the model to more efficiently capture complex dependence structure in observed variables.

This ability to capture complex dependence, as well
as conform to different distributional shapes, is attractive for
multiple imputation contexts, as it  helps the imputer to preserve
structure in the data that he or she may not have anticipated but may
be important to analysts.  Mixture models have been suggested previously for multiple imputation of missing
categorical data \citep[e.g.,][]{Vermunt2008, Gebregziabher2010, Si2013,
  Manrique-Vallier2012, Manrique-Vallier2012a, si:reiter:hillygus:14} and missing continuous data \citep[e.g.,][]{Bohning2007,
  Elliott2007, Kim2013}. To our knowledge, mixture models have not been used to impute mixed categorical and continuous data.

The remainder of the article proceeds as follows.  In Section
\ref{sec:motivation},  we illustrate some of the complex
distributional features of the variables in the SIPP, and we discuss
how existing multiple imputation routines could struggle to capture
such features. In Section \ref{sec:model}, we introduce the HCMM-LD\
including specification of prior distributions, and discuss related
nonparametric Bayesian models. %
In Section \ref{sec:sipp-sim}, we present results of a repeated sampling
simulation using complete cases from an existing SIPP panel,
illustrating the potential for improved performance of multiple imputation using the
HCMM-LD\ over a default application of MI by chained
equations \citep{Raghunathan2001,VanBuuren1999}. In Section
\ref{sec:msipp}, we apply the HCMM-LD\ to multiply-impute missing values
in the field test data as well as the representative subsample of the production SIPP. Some
conclusions about the comparability of the two designs change
after accounting for the missing data.  Finally, in Section
\ref{sec:conclusion}, we conclude with a discussion of extensions and
future work.

\section{The Challenges of Imputing SIPP Data}\label{sec:motivation}

\begin{figure}
 \centering
 \includegraphics[width=.9\textwidth]{./fig/earn_by_hrs_edu.pdf}
 %
 \caption{Log monthly earnings from SIPP, by usual hours worked and education level}
 \label{fig:earn_by_hrs_edu}
\end{figure}

SIPP is characteristic of many surveys in that it includes many
categorical variables and a smaller number of continuous variables, with
complicated dependence and nonstandard distributions. For example, using public-use data from the 2008 SIPP panel, Figure \ref{fig:earn_by_hrs_edu} displays
plots of (log) total earnings by usual hours worked and education level. The
distribution of income varies across levels of the discrete variables.
 The earnings distribution is skewed right when usual hours $\leq 10$, whereas it
eventually becomes slightly skewed left as the number of hours increases. In the
 first three panels, increasing education level is associated with increased
 dispersion in the distribution of log earnings. In the last panel, increased
 education is primarily associated with a location shift in earnings.
There is also evidence of higher-order dependence in the distributions
of the categorical variables. Table \ref{tab:loglm} shows analysis of deviance
tables for one, two, and three way loglinear models fit to a few
subsets of the categorical variables. All indicate some evidence of
interactions.

\begin{table}[t]
\caption{Analysis of deviance tables for loglinear models fit to subsets of the SIPP data.}\label{tab:loglm}
\centering
\begin{tabular}{lrrrrr}

 \multicolumn{6}{c}{Race, sex, education level, hourly}\\
  \hline
 & Resid. Df & Resid. Dev & Df & Deviance & Pr($>$Chi) \\
  \hline
\multicolumn{6}{l}{Race, sex, education level, hourly}\\
$\,\,\,$1 way & 108 & 10191.25 &  &  &  \\
$\,\,\,$  2 way & 69 & 211.50 & 39 & 9979.76 & $<10^{-6}$ \\
$\,\,\,$  3 way & 20 & 39.92 & 49 & 171.58 & $<10^{-6}$ \\
 &  & &  &  &  \\
 \multicolumn{6}{l}{Marital status, usual hours, sex, no. own children}\\
$\,\,\,$1 way & 132 & 6350.60 &  &  &  \\
$\,\,\,$  2 way & 91 & 1383.23 & 41 & 4967.36 & $<10^{-6}$ \\
$\,\,\,$  3 way & 30 & 168.83 & 61 & 1214.40 & $<10^{-6}$ \\
 \hline

\end{tabular}
\end{table}

Given these complex distributional features, what sort of models might
one use for imputation of missing values?  One possible approach is to use
a general location model (GLOM) \citep{Olkin1961,Little1985,Schafer1997}. For
continuous variables $Y$ and discrete  variables $X$,  the GLOM assumes that $(Y\mid X=x)\sim
N(\mu_x, \Sigma_x)$ and $X\sim \pi$ with $\pi\sim Dir(\alpha)$; see
also \cite{Liu1998} who generalize the $(Y\mid X)$ model to the class
of elliptically symmetric distributions. Estimation under this model
is infeasible unless each cell of the table implied by $X$ contains a large number of
observations.  Thus, imputers typically impose further constraints,
most often that $\Sigma_x\equiv \Sigma$ for all $x$,
$\mu_x = D(x)B$ for a matrix of regression coefficients $B$ and design
vector $D(x)$, and $\pi$ satisfies loglinear constraints that include
interactions only up to a certain order.  Multivariate
normality and common covariance structure seem unlikely to fit the
types of features apparent in Figure \ref{fig:earn_by_hrs_edu}.
Further, Table \ref{tab:loglm} suggests that it would be easy to
miss key interactions when selecting the loglinear model.  Thus,
the GLOM seems overly restrictive for the SIPP data.

An alternative approach  is to specify a sequence of univariate models
for each variable subject to missingness conditional on subsets of
the other variables, e.g., impute $a$ from $f(a \mid b,c)$, impute $b$
from $f(b \mid a,c)$, and impute $c$ from $f(c \mid a,b)$. This is
known as the ``chained equations'' or ``fully-conditional'' approach
\citep{Raghunathan2001,VanBuuren1999}.
While multiple imputation by chained equations (MICE) approaches have proven to be quite useful for
many datasets, they can be challenging to use
effectively for data with complex dependence like the
SIPP.  For example, typical applications of MICE use
multinomial logistic regressions for the categorical
variables.  Relationships between an outcome and the
remaining predictors may be nonlinear and involve interaction effects;
these can be difficult to find when the data have more than a handful
of variables (that may also be subject to missingness). Similar challenges arise when specifying models for continuous data, even with semiparametric extensions like predictive mean matching \citep{Little1988}.
Additionally, %
the selected conditional models may be incompatible; that is, there may not be any joint model with the specified conditionals \citep{Liu2014}.
This may result in imputation procedures with undesirable theoretical properties \citep{Si2013}.

A third and related approach is to specify a coherent joint distribution as a
sequence of conditional models \citep{ibrahimlips, ibrahim, ibrahim:chen:lip:herr}, for example $f(a, b,
c) = f(a) f(b \mid a) f(c \mid b, a)$.
Compared to typical chained equations
approaches, this has the advantage of resulting in a fully coherent joint
distribution.  However, it still can be challenging to find and model complex
distributional features, particularly for models with many predictors.  Additionally,
different conditioning sequences for the variables could result in different fits,
and the imputer may not have good information to help choose an order.

 %

\section{Multiple Imputation via the HCMM-LD}\label{sec:model}

For $i=1,\dots,n$ sampled individuals, let
$X_i = (X_{i1},\dots, X_{ip})'$ be a vector of $p$
categorical variables for individual $i$, with each $X_{ij} \in
\{1,\dots, d_j\}$, and let $Y_i = (Y_{i1},\dots, Y_{iq})'$ be a vector of $q$ continuous responses taking values in $\mathbb{R}^q$.
We use $x_i$ and $y_i$ for specific values taken by $X_i$ and $Y_i$.
We also use superscript $\mathcal{X}$ and $\mathcal{Y}$ to signify that some parameter or latent variable is a component of the
model for $X$ or $Y$, respectively.

\subsection{The HCMM-LD for Imputing Mixed Data}

As noted in Section 1, mixture models have proven valuable for imputing multivariate missing data that are
strictly continuous or categorical.
The HCMM-LD\ fuses existing mixture models for strictly continuous or categorical data into a larger hierarchical model.
Thus, we begin with a brief
summary of these existing mixture models and discuss the shortcomings of various ``intuitive'' ways to combine them. We
present the HCMM-LD\ in Section \ref{sec:indexmodel}.

For imputing multivariate continuous data, \cite{Kim2013} use a truncated Dirichlet process (DP) mixture of normal distributions.
For $i=1,\dots,n$, let $H_i^{(\mathcal{Y})} \in \{1, \dots, {k^{\mathcal{(Y)}}}\}$ be the mixture component index for record $i$. This model assumes that
\begin{equation}
(Y_i\mid H_i^{(\mathcal{Y})}=\hy, \{(\mu_\hy, \Sigma_\hy) : 1\leq \hy\leq {k^{\mathcal{(Y)}}}\}) \sim N(\mu_\hy, \Sigma_\hy).\label{eq:ymodel}
\end{equation}
The prior distribution for $H_i^{(\mathcal{Y})}$ is a truncated version of the stick-breaking construction for the DP \citep{Sethuraman1994}, introduced in \cite{Ishwaran2001}:
\begin{gather}
\Pr(H_i^{(\mathcal{Y})}=\hy) = \byy{\phi_{\hy}}\\
\byy{\phi_{\hy}} = \byy{\xi_\hy}\prod_{l<\hy}(1-\byy{\xi_l}),\ \{\byy{\xi_\hy}: 1\leq \hy\leq {k^{\mathcal{(Y)}}}-1 \}\overset{iid}{\sim} Beta(1, \byy{\beta}),\
\byy{\xi_{{k^{\mathcal{(Y)}}}}}\equiv 1.\label{eq:Kip}
\end{gather}

For imputing multivariate categorical data, \cite{Si2013} adopt a truncated version of the DP mixture of product multinomials (MPMN) proposed
by \cite{Dunson2009}.
For $i=1,\dots,n$, let $H_i^{(\mathcal{X})} \in \{1, \dots, {k^{\mathcal{(X)}}}\}$ be the mixture component index for record $i$,
and let $\Pr(X_{ij} = x_{ij} \mid H_i^{(\mathcal{X})} = \hx) = \psi_{\hx x_{ij}}^{(j)}$. This model assumes that
\begin{align}
 \Pr(X_i = x_i \mid H_i^{(\mathcal{X})} = \hx, \{\psi_\hx : 1\leq \hx\leq{k^{\mathcal{(X)}}}\}) &= \prod_{j=1}^{p}\psi_{\hx x_{ij}}^{(j)}\label{eq:dx},
\end{align}
where, for each $1\leq \hx\leq {k^{\mathcal{(X)}}}$,  $\psi_\hx=\{ \psi_{\hx}^{(j)}: 1\leq j \leq p\}$ and each
$\psi^{(j)}_\hx = (\psi^{(j)}_{\hx 1}, \dots, \psi^{(j)}_{\hx d_j})'$ is a probability vector.
The prior on $\Pr(H_i^{(\mathcal{X})}=\hx)$ is another truncated stick breaking process:
\begin{gather}
\Pr(H_i^{(\mathcal{X})}=\hx) = \byx{\phi_\hx}\\
\byx{\phi_\hx} = \byx{\xi_\hx}\prod_{l<\hx}(1-\byx{\xi_l}),\ \{\byx{\xi_\hx}: 1\leq \hx\leq {k^{\mathcal{(X)}}}-1 \}\overset{iid}{\sim} Beta(1, \byx{\beta}),\ \byx{\xi_{k^{\mathcal{(X)}}}}\equiv 1.\label{eq:Hip}
\end{gather}

Given their success as imputation engines, it seems promising to fuse these two models into a coherent joint
distribution and MI engine for mixed data.
One approach is to assume the variables arise as in \eqref{eq:ymodel} and \eqref{eq:dx} with shared components
$H_i^{(\mathcal{X})}=H_i^{(\mathcal{Y})}\equiv H_i$, that is,
\begin{gather}
(Y_i\mid H_i=h,-) \sim N(\mu_h, \Sigma_h),\
\Pr(X_i = x_i \mid H_{i} = h, -) =\prod_{j=1}^{p}\psi_{hx_{ij}}^{(j)}.
\end{gather}
This model makes strong \emph{local independence} assumptions, namely that $Y \id X \mid H$. This puts a significant burden on
the mixture components. They must simultaneously capture non-normality in the distribution of $Y$, dependence between
 $Y$ and $X$, and dependence within $X$.  Doing so typically requires a large number of components and a commensurate
amount of data. For example, since $X$ is categorical the true mean function can be written as ${E(Y\mid X=x)=\tilde D(x)\tilde{B}}$, where $\tilde D(x)$ is the true design vector and $\tilde{B}$ is the matrix of true regression coefficients.
The
model has to include components at each distinct value of $\tilde D(x)\tilde{B}$---for all possible values of $x$---just to model the mean function, with further
components to capture non-Gaussian structure in $Y$ and dependence in $X$.

This burden can be alleviated somewhat by allowing the means to depend on $X$ as in the general location model: $\mu_h(x) = D(x)B_h$, with $D$ encoding main effects and possibly interactions. However, when $p>q$ as is common in survey data, the number of components required to adequately model dependence in
$X$ tends to be much larger than that required to model $Y$, particularly since this model allows for local dependence
in $Y$ (through the covariance matrices) but not in $X$.

An alternative approach is to use separate component indices and independent
prior distributions for $\Pr(H_i^{(\mathcal{X})}=\hx)$ and $\Pr(H_i^{(\mathcal{Y})}=\hy)$, as in \eqref{eq:ymodel}-\eqref{eq:Hip}, but add $(X,Y)$ dependence by setting $\mu_\hy(x) = D(x)B_{\hy}$.
We have
 \begin{gather}
(Y_i\mid X_i = x_i, H_i^{(\mathcal{Y})}=\hy,-) \sim N(D(x_i)B_\hy, \Sigma_\hy),\label{eq:ymodelwithx}\\
 \Pr(X_i = x_i \mid H_i^{(\mathcal{X})} = \hx, -) =\prod_{j=1}^{p}\psi_{\hx x_{ij}}^{(j)}.\label{eq}
 \end{gather}
This model enforces restrictive assumptions about the relationship between $Y$ and $X$. For example, we would
have $E(Y\mid X=x) =  D(x)\left[\sum_{\hy=1}^{{k^{\mathcal{(Y)}}}} B_\hy\byy{\phi_\hy} \right]$, so that the model is unable to capture interactions not
already coded in $D(x)$.

To construct the HCMM-LD, we use \eqref{eq:ymodelwithx} and \eqref{eq} as the data models.  However, rather
than choose between common components or independent components, we use
a hierarchical prior distribution that maintains the desirable features of both, while
incorporating new forms of local dependence. We now outline this hierarchical prior distribution for $(H_i^{(\mathcal{X})}, H_i^{(\mathcal{Y})})$.

\subsubsection{Hierarchical prior for component indexes}\label{sec:indexmodel}

Let $Z_i$ be a third component index such that $1\leq Z_i\leq {k^{\mathcal{(Z)}}}$.  We assume $H_i^{(\mathcal{X})}$ and $H_i^{(\mathcal{Y})}$ are independent given $Z_i$, so that
\begin{gather}
\Pr(H_i^{(\mathcal{X})}=\hx, H_i^{(\mathcal{Y})}=\hy \mid Z_i=z)
 = \byx{\phi_{z\hx}}\byy{\phi_{z\hy}}\label{eq:hmodel}\\
 \Pr(Z_i=z) = \lambda_z.\label{eq:zmodel}
\end{gather}
Here each $\byx{\phi_z} = \left(\byx{\phi_{z1}},\dots,\byx{\phi_{z{k^{\mathcal{(X)}}}}}\right)'$ and
$\byy{\phi_z} = \left(\byy{\phi_{z1}}, \dots,\byy{\phi_{z{k^{\mathcal{(Y)}}}}}\right)'$ are probability vectors.
Both are assigned independent truncated stick breaking priors.  For $1\leq z\leq {k^{\mathcal{(Z)}}}$, we have
\begin{gather}
\byx{\phi_{z\hx}} = \byx{\xi_{z\hx}}\prod_{l<\hx}(1-\byx{\xi_{z\hx}}),\ \{\byx{\xi_{z\hx}}: 1\leq \hx\leq {k^{\mathcal{(X)}}}-1 \}\overset{iid}{\sim} Beta(1, \byx{\beta}),\ \byx{\xi_{k^{\mathcal{(X)}}}}\equiv 1.\\
\byy{\phi_{z\hy}} = \byy{\xi_{z\hy}}\prod_{l<\hy}(1-\byy{\xi_{z\hy}}),\ \{\byy{\xi_{z\hy}}: 1\leq \hy\leq {k^{\mathcal{(Y)}}}-1 \}\overset{iid}{\sim} Beta(1, \byy{\beta}),\ \byy{\xi_{k^{\mathcal{(Y)}}}}\equiv 1.
\end{gather}
Marginalizing over $Z$ gives $\Pr(H_i^{(\mathcal{X})}=\hx, H_i^{(\mathcal{Y})}=\hy) = \sum_{z=1}^{{k^{\mathcal{(Z)}}}} \lambda_z\byx{\phi_{z\hx}}\byy{\phi_{z\hy}}$, inducing dependence between the latent component membership indicators.

The top-level mixture probabilities $\lambda=(\lambda_1,\lambda_2,\dots,\lambda_{{k^{\mathcal{(Z)}}}})'$ are also assigned a truncated stick breaking process:
\begin{align}
\lambda_z = \byz{\xi}_z\prod_{l<z}(1-\byz{\xi}_l),\ \{\byz{\xi}_z: 1\leq z\leq {k^{\mathcal{(Z)}}}-1 \}\overset{iid}{\sim} Beta(1, \alpha),\ \byz{\xi}_{{k^{\mathcal{(Z)}}}}\equiv 1.
\end{align}
\cite{Banerjee2013} establish that as $({k^{\mathcal{(Z)}}},{k^{\mathcal{(X)}}},{k^{\mathcal{(Y)}}})$ all approach $\infty$, this is a well-defined prior distribution, which they call an infinite tensor factorization (ITF) prior.
We assign $\alpha, \byx{\beta}$, and $\byy{\beta}$ independent Gamma prior distributions with shape and rate parameters equal to 0.5. A convenient strategy for choosing the truncation levels $({k^{\mathcal{(Z)}}},{k^{\mathcal{(X)}}},{k^{\mathcal{(Y)}}})$ is to pick moderate initial values, increasing them if the number of occupied components approaches its upper bound. Appropriate values will depend on the dataset; for all the models fit in this paper we take ${k^{\mathcal{(Z)}}}=15,\ {k^{\mathcal{(X)}}}=90$, and  ${k^{\mathcal{(Y)}}}=60$, which we found to be conservative {upper bounds. Generally, the HCMM-LD\ is insensitive to specific choices of $({k^{\mathcal{(Z)}}}, {k^{\mathcal{(X)}}}, {k^{\mathcal{(Y)}}})$ provided that they allow for unoccupied components. }

\subsubsection{Data model priors}

We next specify prior distributions for the parameters in \eqref{eq:ymodelwithx} and \eqref{eq}.  For each $\psi_\hx^{(j)}$, we use independent Dirichlet distributions,
\begin{equation}
 \psi^{(j)}_{\hx} \overset{iid}{\sim} Dir(\gamma_{\hx 1}^{(j)}, \dots, \gamma_{\hx d_j}^{(j)}).
\end{equation}
Reasonable default choices for the hyperparameters include setting $\gamma_{\hx}^{(j)} = (1,\dots,1)$ or
$\gamma_{\hx}^{(j)} = (1/d_j,\dots,1/d_j)$.  Both represent relatively vague information about the within-component probabilities. In practice, we find that posterior predictive distributions are usually insensitive to this choice, and we
use the latter going forward.

For the parameters in each $Y$-component, we use hierarchical normal-inverse Wishart priors. The hierarchical priors are an alternative to more restrictive models, recognizing that many components will have a relatively small number of data points and that elements of $B_{\hy}$ in particular may be poorly estimated. We have
\begin{equation}
 \{(B_{\hy}, \Sigma_{\hy})\}\overset{iid}{\sim} MatN( B_0, I, T_B)\times IW(v, \Sigma)
\end{equation}
\begin{equation}
 (B_0, \Sigma)\sim MatN( 0, I, \sigma^2_{0\beta}I)\times W(w, \Sigma_0).
\end{equation}
Here, $MatN(M, \Phi, \Sigma)$ is the matrix normal distribution, i.e. the distribution of the $p^*\times q$ dimensional matrix $M + \Phi^{1/2}\Omega\Sigma^{1/2}$ when $\Omega$ is $p^*\times q$ with $\omega_{ij}\overset{iid}{\sim} N(0,1)$. We assume that $T_B =\diag(1/\tau_{1},\dots, 1/\tau_{q})$, and assign $\tau_1,\dots \tau_q$ independent $G(0.5, 0.5)$ priors. In applications we find the posterior predictive distributions to be insensitive to this choice.
To complete the hyperprior, we use the fact that $E(\Sigma_h) = \frac{v}{w-q-1}\Sigma_0$.
We center and scale each element of $Y$ marginally
and take $v=q+1$, $w=q+2$, and $\Sigma_0 = \frac{1}{q+1}I$ throughout. In sufficiently large samples, inferences are insensitive to the choice of $\sigma^2_{0\beta}$; we use $10$.

\subsection{Properties of the HCMM-LD\ }\label{sec:modelprop}

\begin{figure}
 \centering
 \includegraphics[trim=0cm 4cm 0cm 4cm, width=.45\textwidth]{./fig/plate.pdf}
 %
 \caption{Model structure of the HCMM-LD.}
 \label{fig:plate}
\end{figure}

{Figure \ref{fig:plate} summarizes graphically the dependence structure of the HCMM-LD.} Marginally, $X$ has a latent class model {of the form
\begin{equation}
 \Pr(X_i = x_i) = \sum_{\hx=1}^{{k^{\mathcal{(X)}}}} \left(\sum_{z=1}^{{k^{\mathcal{(Z)}}}} \lambda_z\byx{\phi_{z\hx}}\right) \prod_{j=1}^{p}\psi_{\hx x_{ij}}^{(j)},\label{eq:marx}
\end{equation}
where the term in parentheses gives the probability for class $s$}. This can capture any multivariate categorical distribution given sufficiently large ${k^{\mathcal{(X)}}}$ (unlike unsaturated loglinear models). Conditional on $Y=y$, $X$ still follows a latent class model but with class probabilities that are functions of $y$. The  conditional distribution of $Y$ for any cell of the $X$ table is a mixture of multivariate normal distributions,
\begin{equation}
 f(Y_i\mid X_i=x_i) =  \sum_{\hy=1}^{{k^{\mathcal{(Y)}}}}
 \frac{w_\hy(x_i)}{\sum_{l=1}^{{k^{\mathcal{(Y)}}}} w_l(x_i)}
 N(Y_i; D(X_i)B_\hy, \Sigma_\hy)\label{eq:ygivenx}
\end{equation}
where $w_{\hy}(x_i) = \sum_{z=1}^{{k^{\mathcal{(Z)}}}} \lambda_z\byy{\phi_{z {\hy}}}
\sum_{\hx=1}^{{k^{\mathcal{(X)}}}}\byx{\phi_{z\hx}}\prod_{j=1}^{p}\psi_{\hx x_{ij}}^{(j)}$.
The marginal distribution of $Y$ is also a mixture of multivariate normals.
 Thus, the HCMM-LD\ can represent a wide variety of shapes for the distribution of $Y$.
Since $w_{\hy}(x_i)$ also appears in the expression for the conditional mean of $Y$,
the HCMM-LD\ can
capture interactions not necessarily encoded in $D$.

 %
 %
The HCMM-LD\  {encodes} local dependence within and between $Y$ and $X$ in several ways{:} The $Y$-component specific regression
functions and covariance matrices allow the relationships between $Y$ and $X$, and within $Y$, to vary by component.
Further, the prior distribution in \eqref{eq:hmodel} - \eqref{eq:zmodel} implies that the HCMM-LD\ is a ``mixture of mixture models.''
Marginalizing over $H_i^{(\mathcal{X})}$ and $H_i^{(\mathcal{Y})}$, the density of $(Y_i,X_i)$ given $Z_i=z$ is
\begin{equation}
f(X_i, Y_i \mid Z_i=z) = \left(\sum_{\hy=1}^{k^{\mathcal{(Y)}}} \byy{\phi_{z\hy}}N(Y_i; D(X_i)B_{\hy}, \Sigma_{\hy}) \right)\left(\sum_{\hx=1}^{k^{\mathcal{(X)}}} \byx{\phi_{z\hx}}\prod_{j=1}^{p}\psi_{\hx X_{ij}}^{(j)}\right)\label{eq:xymidz},
\end{equation}
{so the joint density is
\begin{equation}
f(X_i, Y_i) = \sum_{z=1}^{{k^{\mathcal{(Z)}}}} \lambda_z\left(\sum_{\hy=1}^{k^{\mathcal{(Y)}}} \byy{\phi_{z\hy}}N(Y_i; D(X_i)B_{\hy}, \Sigma_{\hy}) \right)\left(\sum_{\hx=1}^{k^{\mathcal{(X)}}} \byx{\phi_{z\hx}}\prod_{j=1}^{p}\psi_{\hx X_{ij}}^{(j)}\right)\label{eq:xy}.
\end{equation}
}

For any $z$, $(X\mid Z=z)$ follows an MPMN model.
 The distribution of $(Y\mid X, Z=z)$ is nearly the ANOVA-DDP model of \cite{DeIorio2004}, except that we relax
their common covariance assumption with the hierarchical prior. From \eqref{eq:xymidz}, we see that within top-level components $Z$
we have local \emph{dependence} within $X$, as well as between $X$ and $Y$ (and within $Y$). Note that $f(X_i, Y_i\mid Z_i=z)$ and $f(X_i, Y_i\mid Z_i=z')$  differ
only in their respective lower-level stick breaking weights, $(\phi^{(y)}_{z},\phi^{(x)}_{z})$ and $(\phi^{(y)}_{z'},\phi^{(x)}_{z'})$, and not in the lower-level parameters ($\{(B_\hy, \Sigma_\hy)\}$ and $\psi_\hx$). This is a parsimonious choice,  somewhat akin to assuming common covariance structures across components in normal mixture models (but much more flexible).

\subsection{Related work}\label{sec:mixlit}

\cite{Dunson2010} extended Dunson's and Xing's (2009) MPMN to mixed data by assuming fully factorized (product) kernels in a DP mixture. This
model is a special case of the HCMM-LD\ with ${k^{\mathcal{(Y)}}}={k^{\mathcal{(X)}}}=1$, diagonal $\Sigma_\hy$, and $D(x_i)=1$. \cite{Dunson2010} note that when the number of variables grows the number of clusters also must grow to accommodate the dependence in the joint distribution. This is due to the local independence assumptions of the
product kernel, which forces all the dependence to be represented through a single cluster index. As described in Section \ref{sec:modelprop}, the HCMM-LD\ is able to avoid such strong local independence assumptions through the use of multivariate normal regression components with full covariance matrices, as well as the structure imposed by the hierarchical prior on the mixture component memberships.

A number of authors have proposed joint mixture models that
include limited local dependence to induce a
prior on one of the conditional distributions. These models decompose the joint kernel into a
conditional kernel for one variable given the others and a marginal product
kernel for predictors \citep{Shahbaba2009a,Molitor2010,Hannah2011}.
Some of these are special cases of the HCMM-LD\ obtained by restricting ${k^{\mathcal{(Y)}}}={k^{\mathcal{(X)}}}=1$ and imposing more structure on the local covariances. These models are less relevant for imputation, where the entire joint distribution is of interest. Moreover, the assumption of local marginal independence between the majority of the variables can lead to the same proliferation of clusters as in
latent class models \citep{Hannah2011}.

\cite{Banerjee2013} introduced the ITF prior to avoid the proliferation of components through \emph{dependent} component assignment in separate univariate mixtures. Compared to the HCMM-LD, this model encodes weaker local
dependence, arising strictly through shared lower-level components within top-level components.
\cite{Wade2011} proposed the enriched DP, which (like the ITF) models dependent cluster assignment.
 The enriched DP separates a joint distribution into a conditional and a marginal,
assigning each  a DP prior distribution where the base measure for the
conditional varies across the marginal. It lacks
the symmetry of the ITF, making it more difficult to interpret the
induced joint distribution and its margins. This is unappealing for our purposes.

The HCMM-LD\ has a number of benefits over existing alternatives. The hierarchical structure on component indices and other local dependence features allow the analyst to avoid the proliferation of clusters. At the same time, the induced marginal and conditional distributions are easy to derive and the HCMM-LD\ has appealing limiting forms (the MPMN model for $X$ and a multivariate regression or ANOVA-DDP for $Y\mid X$). Computation via MCMC is also straightforward, as detailed in the supplementary material.

\section{Repeated Sampling Simulation Studies}\label{sec:sipp-sim}
To evaluate the performance of HCMM-LD\ in multiple imputation (MI), we
conducted several repeated sampling simulation studies on a constructed population
taken from the first wave of the 2008 SIPP panel. We define the
population as individuals who reported positive income from work
during the reference period in Wave 1, excluding records with
missing entries.
The constructed population consists of $N$=30,507
respondents.  With guidance from Census Bureau researchers, we select the two continuous
and eleven categorical variables displayed in
Table \ref{tab:sippvars}. We use a modest number of variables to
make a large repeated sampling study more efficient while keeping the problem
challenging. For example, the implied contingency table has over 7 million
cells and is very sparse.  %

Below we present comparisons of the HCMM-LD\ versus a fully conditional approach, as implemented in the R package \texttt{mice} \citep{VanBuuren2011}. We compare against a fully conditional approach as these have been repeatedly shown to perform at least as well as existing joint models for MI \citep[e.g.,][]{VanBuuren2007,lee2010multiple,kropko2014multiple} and are in widespread use.
In the online supplement we also compare to a variant of the general location model; its performance is dominated by that of the HCMM-LD\ and MICE. The supplement also includes a simulation study comparing the HCMM-LD\ and MICE under missingness completely at random (MCAR). Overall conclusions under MCAR are similar to those below, but the performance difference is greater under MCAR since all variables were subject to missingnes in that case.

\begin{table}[t]
\caption{Variables in the repeated sampling simulation study}\label{tab:sippvars}

    \begin{tabular}{|l|l|}
    \hline
    Variable                           & Levels                                  \\ \hline
    Total monthly earnings from employment     & Continuous                              \\
    Age                                & Continuous                              \\
    Sex                             & 2                                       \\
    Race                               & 5                                       \\
    Marital Status                     & 6                                       \\
    Born in the US                     & 2                                       \\
    Number of own children in the home & 4 (0,1,2, or 3+)                        \\
    Education level                    & 6                                       \\
    Occupation                         & 23                                      \\
    Worker Class                       & 3 (Private, Nonprofit, Government)      \\
    Union                              & 2                                       \\
    Hourly                             & 2                                       \\
    Usual Hours worked                 & 9 (0-80 in increments of 10 hours, 80+) \\ \hline
    \end{tabular}
\end{table}

\subsection{MAR simulation study design}
We create 500 datasets by taking simple random samples of size
$n=6,000$.  In each dataset, we let a random sample of 180 observations be complete cases. Age and sex are completely observed. Let $R_{i,\text{var}}=1$ when the variable ``var'' is missing for observation $i$ and $0$ otherwise. Define $U_{i} = \ind{\text{sex}_i=\text{``male''}}$. We sample
 $R_{i,\text{earn}}$ and $R_{i,\text{child}}$ from Bernoulli distributions with probabilities derived from
\begin{align*}
\logit[\Pr(R_{i,\text{earn}}=1)] &= -0.25 + 0.5U_{i} - \left(\frac{\text{age}_i-25-25U_{i}}{25}\right)^2\\
\logit[\Pr(R_{i,\text{child}}=1)] &= -1.5U_{i} - \left(\frac{\text{age}_i - 40 + 10U_{i}}{30 + 10U_{i}}\right)^2.
\end{align*}
We partition the remaining variables into two blocks: demographic variables (race, marital status, born in US) and variables directly related to employment (education, occupation, worker class, union, hourly, hours worked). For each variable $j$ in the demographic block, we sample each $R_{ij}$ from  Bernoulli distributions with probabilities derived from
\begin{equation}
\logit[\Pr(R_{ij}=1)] = -1 + 0.7R_{i,\text{child}} + 1.25\kappa_{ij},
\end{equation}
where $\kappa_i$ is a $3$-dimensional vector drawn from a normal distribution with mean 0, unit variances and all correlations equal to 0.3. For each variable $j'$ in the employment block, we sample each case's $R_{ij'}$ from Bernoulli distributions with probabilities depending on  $R_{i,\text{earn}}$ instead of $R_{i,\text{child}}$:
\begin{equation}
\logit[\Pr(R_{ij'}=1)] = -1 + 0.7R_{i,\text{earn}} + 1.25\omega_{ij'},
\end{equation}
where $\omega_i$ is a $6$-dimensional vector drawn from a normal distribution with mean 0, unit variances and all correlations equal to 0.3. %

In this MAR design, approximately 1/3 of the entries are missing for each variable (except age and sex) and approximately 5\% of cases are complete. %
The resulting imputation problem is challenging, as highly correlated variables are more likely to be missing simultaneously.
The MAR mechanism results in biased available case estimates; for example, regressing log earnings on $U_m$ gives estimates of the coefficient around 0.25 (SE 0.02) in the available cases, compared to a true value of about 0.36.

\subsubsection{Generating imputations}
Within each of the 500 simulated datasets we create $M=10$ multiple imputations
with the HCMM-LD.  We use the default prior distributions described
in Section \ref{sec:model}, after standardizing the continuous
variables, and include main effects for each categorical variable in $D(X)$.
We estimate the HCMM-LD\ for each dataset using 200,000 MCMC iterations from the
Gibbs sampler described in the supplemental material, discarding the
first $100,000$ iterations and keeping the imputations from every
$10,000^{th}$ iteration thereafter. This is very conservative;
examination of a handful of datasets suggests that these numbers
could be reduced by at least half without impacting the results. In
practice, of course, imputers should carefully examine MCMC diagnostics of
relevant identified parameters, such as marginal means, quantiles, and
variances or covariances in the completed datasets. We ran the
simulations in a heterogeneous cluster environment, so the run times
varied.  As a reference, a 2014 MacBook Pro can complete 10,000 iterations of
the MCMC sampler in about 20 minutes. Our implementation could be made much more efficient; we discuss scalability in Section \ref{sec:conclusion}.

With each incomplete dataset, we also implement multiple imputation via
chained equations using the R package \texttt{mice}. Our goal is to compare default
applications of the software to a default application of the HCMM-LD, so we did not alter any of the options
to \texttt{mice} other than to set $M=10$. The default
procedure imputes continuous variables via predictive mean matching
\citep{Little1988} and uses logistic regressions to impute discrete
variables. Each conditional model includes a main effect for every
other variable.  After imputing the data with both procedures, we obtain MI inferences for a number of estimands using the methods in
\citet{Rubin1987}.  We compute completed-data estimates and standard errors using the
\texttt{survey} package in R \citep{Lumley2004},
incorporating a finite population correction.%

 %

\subsubsection{Evaluation metrics}

{We evaluate the competing imputation methods based on the performance of the MI pooled estimate and associated confidence interval
for a range of estimands. For each estimate, the ``true'' value is the corresponding quantity computed in the population of $N$ individuals.
Ideally, under repeated sampling and realizations of the nonresponse process, and across a range of estimands, the imputation methods yield
completed datasets for which 1) pooled estimates are approximately unbiased for the corresponding population quantities, and 2)
pooled confidence intervals with level $\alpha$ contain their true population values at least $(1-\alpha)\%$ of the time \citep{Rubin1996}.
Thus, while the proposed imputation method is derived from a Bayesian model, the ultimate evaluations are frequentist;
see \cite{Rubin1987,Rubin1996} for justification of this perspective.}

\subsection{Results}

We begin by examining the means of log monthly earnings by age
(discretized into 10 year intervals except for $<18$, $18-25$, and
$65+$), sex and presence of own children.
We restrict to cells in the
table formed by the three categorical variables with expected counts
of at least 30. We work on the log scale rather than with untransformed incomes, as
the skewness of the income distribution makes normal approximations
more likely to hold.%
                                %
                                %
                                %

Figure \ref{fig:age-sex-kid-ci} shows the coverage rates and average
width of 95\% multiple imputation confidence intervals. For most cells the pooled confidence intervals have approximately the correct coverage (the cluster of points around (0.95, 0.95) on the left hand side of Fig. \ref{fig:age-sex-kid-ci}). However, there are three cells where the MICE-constructed imputations yield substantially lower coverage than under the HCMM-LD. On average the pooled confidence intervals have similar widths, suggesting that bias in MICE's imputations drive the poor coverage. This is confirmed by Figure \ref{fig:age-sex-kid-bias}, which shows that while neither method has uniformly lower bias, the range of bias under the HCMM-LD\ is much smaller.

\begin{figure}

{\centering \includegraphics[width=.4\linewidth]{fig/mar_res6000-mean_age_kid_sex_cover1}
\includegraphics[width=.4\linewidth]{fig/mar_res6000-mean_age_kid_sex_cover2}

}
\caption{(Left) Coverage rate of pooled nominal 95\% CI for mean log monthly earnings by age, sex, and own children in the home (Yes/No) (Right) Average CI width
of 95\% CI.}
\label{fig:age-sex-kid-ci}
\end{figure}

\begin{figure}

{\centering \includegraphics[trim={0 0.5cm 0 0}, width=.35\linewidth]{fig/mar_res6000-mean_age_kid_sex1}
\includegraphics[trim={0 0.5cm 0 0}, width=.35\linewidth]{fig/mar_res6000-mean_age_kid_sex2}

}

\caption{Standardized and percent bias of pooled
  estimates of mean log monthly earnings by age, sex, and own children
  in the home (Yes/No). Each line represents a cell mean, with the
  left and right endpoints at the bias under MICE and HCMM-LD,
  respectively.}
\label{fig:age-sex-kid-bias}
\end{figure}

These are not especially small cells, although they do have somewhat higher probabilities of missingness for the own child and income variables (around 0.5 and 0.4, respectively).
The same estimates are problematic in the MCAR simulation (see the supplementary material), so this is not merely a function of
 the MAR mechanism used here.
Rather, it appears to be a function of complicated relationships among the variables involved.

Age and income have a relationship that the MICE imputations evidently
capture less effectively than the HCMM-LD\ imputations. For example, earnings tend to be lowest in the young (SIPP records earnings information on
respondents 15 or older), increasing during working years and falling
off again as those who can afford to retire do so. Additionally, the
variance in earnings is low in the younger cohort, roughly stable
through the working years, and increasing near and after retirement
age. Interactions also appear to be at play; the effect of
having their own child in the home varies across the respondent's age,
probably due in part to its high correlation with the age of the children, and
across the sexes as well. For example, the population difference in
log wages between those with children versus no children for 18-24 year old women is -0.159, whereas  for 35-44 year
old women it is -0.076. In men the population differences are -0.064 for 18-24 year olds and 0.232 for 35-44 year olds.

\subsubsection{Regression Coefficients}

Next we consider linear regressions of log earnings on age, sex, usual
hours worked (recoded as $<30$, 30-60, and $60+$), and indicators for
marriage and own child under 18 in the
household. To begin we fit a model including an age squared term as
well as two- and three-way interactions between sex, own child, and
marital status. Figure \ref{fig:regms3sq} displays MI
estimates of the coefficients and the average width of their
confidence intervals. {The HCMM-LD\ imputations result in better
repeated sampling properties overall. Neither method was modifed to anticipate the nonlinear relationship between age and income, although both have some ability to capture such relationships. MICE's predictive mean matching effectively borrows residuals from cases with similar predicted means, providing some protection against model misspecification \citep{Little1988}, whereas the HCMM-LD\ specifically intends to capture complex relationships between the variables.} From Figure \ref{fig:regms3sq} it is clear that the HCMM-LD\ is more successful at capturing this structure, with coverage nearer the nominal level for age and age squared (and all other coefficients), despite age being completely observed.

\begin{figure}

{\centering \includegraphics[width=.4\linewidth]{fig/mar_res6000-regms3sq1}
\includegraphics[width=.4\linewidth]{fig/mar_res6000-regms3sq2}

}

\caption{(Left) Coverage rate of pooled nominal 95\% CI for the regression with three-way interaction and age squared, including fpc. (Right) Average width
of 95\% CI.}
\label{fig:regms3sq}
\end{figure}

We also considered the same model excluding the age squared term.
Figure \ref{fig:regms3} shows that the results are largely similar for the former, with coverage generally improved overall but both methods struggling on the coefficients for own child and its interaction with the indicator of being married. Bias and average widths of confidence intervals are generally similar between the two methods on all the coefficients. A notable exception is the coefficient on the indicator variable for working over 60 hours, for which MICE achieves 85\% coverage to HCMM-LD's 96\%. The difference is driven by bias; the true population coefficient is 0.23, and the average pooled estimate using the MICE imputations is 0.18 versus 0.23 under HCMM-LD. The effect persists even in the model including only main effects (coverage of 82\% under MICE, versus 97\% under HCMM-LD). Here the true coefficient is 0.25, and the average point estimate from MICE is 0.18 versus 0.24 in the HCMM-LD. Coverage, widths of CIs and bias were essentially identical under both methods for the other coefficients. We had expected MICE to dominate in the main effects model since this is a submodel of the linear model MICE used to impute income. The relatively poor performance appears to
be due to the small sample size of this group (807 in the
population) and large true effect,
which combine to make predictive mean matching less effective.

\begin{figure}

{\centering \includegraphics[width=.4\linewidth]{fig/mar_res6000-regms31}
\includegraphics[width=.4\linewidth]{fig/mar_res6000-regms32}

}

\caption{(Left) Coverage rate of pooled nominal 95\% CI for regression with three-way interaction \emph{without} age squared, including fpc. (Right) Average width
of 95\% CI.}
\label{fig:regms3}
\end{figure}

\subsubsection{Conditional Frequencies}

We also examine the quality of categorical imputations by estimating
cell frequencies of categorical variables. We restrict to cases where
$E(n_c)\times p_c\geq10$ and $E(n_c)\times (1-p_c)\geq10$, where $p_c$ is
the true proportion and $n_c$ is the cell size in a simple random sample, to make the normal approximation more plausible. Figure \ref{fig:prop_own_child} displays results from estimating the proportion of respondents with their own child under 18 in the home by sex, race and age. Recall that only race and the presence of the respondent's own child have missing values.

The HCMM-LD\ based imputations perform much better than MICE. Coverage rates are uniformly better under the HCMM-LD\ with CIs of comparable width.
Coverage rates for the HCMM-LD\
never drop below 84\% (versus 71\% for MICE in that case), and the difference is dramatic for a few estimands. Figure \ref{fig:prop_own_child_cov_by_n} shows that MICE
has very good or very poor coverage in large cells, consistent with
the lack of coverage arising from misspecification bias. The HCMM-LD\
tends to have slightly lower coverage in these larger cells than in the smaller cells, but not nearly to the extent of MICE.
\begin{figure}
{\centering \includegraphics[width=.4\linewidth]{./fig/mar_res6000-prop_own_kid_sex_race_age_cover_N1}
\includegraphics[width=.4\linewidth]{./fig/mar_res6000-prop_own_kid_sex_race_age_cover_N2}

}
\caption{(Left) Coverage rate of nominal 95\% CIs for proportion with
  own child $<18$ in the household by age, race and sex. (Right) Average width
of 95\% CI.}
\label{fig:prop_own_child}
\end{figure}

\begin{figure}
{\centering \includegraphics[width=.55\linewidth]{fig/mar_res6000-prop_own_kid_sex_race_age}

}
\caption{Coverage by expected cell size for proportion with own child $<18$ in the household by age, race and sex. Lines connect the coverage rates that correspond to the same estimand. Blue dot-dashed lines indicate that the HCMM-LD\ coverage is closer to 95\% than MICE, with red dashed lines indicating the reverse.}
\label{fig:prop_own_child_cov_by_n}
\end{figure}

\section{Evaluating the SIPP Redesign}\label{sec:msipp}

We now evaluate the agreement between the data from the field test and the data from the constructed sample of the
2008 production SIPP panel. For brevity, we use SIPP to refer to the subset of the production panel and SIPP-EHC to refer to
the data from the field test. We focus on a subset of the data, namely household heads in 2010 from the SIPP-EHC and a
contemporaneous wave of the SIPP subsample. The sample sizes are 2,588 for the SIPP-EHC and 3,665 for SIPP.
Previously, Census Bureau researchers compared complete-case estimates from SIPP-EHC to those from production SIPP,
 and also to administrative records where available \citep{USCensus2013}. However, most
 variables have missing values, and for some variables the missingness is substantial as evident in Table \ref{tab:msippvar}.

\begin{table}[tdp]
\begin{center}
\caption{Variables used from field test and production panel, and their fractions of missing data. An * indicates that the missing data percentage is computed as a fraction of the units known to be in-universe; for example, the percentage reported for monthly earnings is the fraction of respondents who indicated employment during the reference period but did not report the earnings amount. These also correspond to the continuous variables; the remainder are discrete.}
\label{tab:msippvar}

\begin{tabular}{l|l|l|l}

Variable Type & Variable & SIPP-EHC & SIPP \\
\hline
Household characteristics & Proxy interview & 0.00\% & 0.00\% \\
 & State & 0.00\% & 0.00\% \\
 & Household composition & 0.00\% & 0.00\% \\
 & No. persons in family & 0.00\% & 0.00\% \\
 & No. children under 18 & 0.00\% & 0.00\% \\
 \hline
Householder characteristics & Sex & 0.00\% & 0.00\% \\
 & Race/Ethnicity & 0.08\% & 4.12\% \\
 & Born in U.S. & 0.12\% & 0.05\% \\
 & Nativity/Citizenship status & 0.12\% & 0.05\% \\
 & Marital status & 0.70\% & 3.30\% \\
 & Disabled & 5.18\% & 4.09\% \\
 \hline
Work/Education & Educational attainment & 1.55\% & 0.00\% \\
 & Enrolled in school & 0.00\% & 0.00\% \\
 & Employment status & 15.96\% & 16.75\% \\
 & Monthly earnings* & 22.70\% & 17.56\% \\
 \hline
Program participation & Health insurance (any) & 2.43\% & 2.62\% \\
 & OASDI & 4.17\% & 1.77\% \\
 & SNAP & 1.85\% & 1.64\% \\
 & SNAP benefit amount* & 58.87\% & 65.00\% \\
 & TANF & 0.62\% & 0.22\% \\
 & SSI & 3.28\% & 3.98\% \\
 & Unemployment insurance & 4.13\% & 0.71\% \\
 \hline
Assets & Own interest bearing account & 6.34\% & 2.21\% \\
 & Own stocks/mutual funds & 5.80\% & 2.29\% \\
 & Own retirement account & 6.38\% & 1.88\% \\
 & Tenure in residence & 0.85\% & 0.03\% \\
 & Own home value* & 28.37\% & 38.57\% \\

\end{tabular}

\end{center}

\end{table}%

Missing data rates are generally similar in SIPP and SIPP-EHC, but missing data patterns vary substantially
between the two surveys.  For example,
Figure \ref{fig:agemis} shows density estimates of respondents' ages by whether their employment status is missing.
In the SIPP sample, respondents with missing employment status are more likely to be younger, whereas in the SIPP-EHC
they tend to be older. In each sample about 16\% of respondents are missing their employment status, so it is
unlikely that these differences are due to sampling variability. In neither case is employment status plausibly missing completely at random, so comparisons based solely on complete cases or pairwise deletion
are unreliable.

\begin{figure}
\begin{center}
\includegraphics[trim={0 0.9cm 0 0}, width=0.7\textwidth]{fig/age-mis}
\end{center}
\caption{Distributions of age in SIPP/SIPP-EHC by missing employment status indicator}
\label{fig:agemis}
\end{figure}

To account for missing data, we generated a set of $M=8$ completed datasets for SIPP and SIPP-EHC.
We used the HCMM-LD with the variables in Table \ref{tab:msippvar}, restricting the design vectors
to main effects only.
We imputed the SIPP-EHC and SIPP
separately to avoid biasing the comparisons.
The continuous variables actually have a spike at zero corresponding to the
unemployed, non-homeowners, or non-participants in SNAP. %
We decompose each of these into a binary indicator of a non-zero value and a continuous variable
 that is treated as missing anywhere the indicator is zero. Imputations for the original variable are constructed as the product
of the indicator and the continuous variable (as in \cite{Heeringa2002}).

We run the MCMC for 130,000 iterations, discarding the first 50,000 and saving a completed dataset
 every 10,000$^{th}$ iteration thereafter. Standard MCMC diagnostics again suggest this is conservative.
We compare the SIPP-EHC and SIPP on estimates of employment status, earnings, home value and SNAP benefit amounts,
 since these variables have significant fractions of missing data. We
 focus primarily on the effect that accounting for missing data has on comparing estimates from SIPP-EHC to the SIPP.
 %
 %

\subsection{Results: The impacts of accounting for missing data}\label{sec:SIPP-EHC:MI}

Figure  \ref{fig:empstat} displays estimates of the proportion of respondents who were
employed at some point during the previous month, computed using the
HCMM-LD\ MI procedure and also using only the
cases with observed values. Compared to the complete case estimates, the MI
estimate is about 1\% higher for the SIPP and 1.5\% lower for
SIPP-EHC; hence, accounting for the missing data attenuates the
apparent differences in the estimates.
This attenuation is concordant with the differential age distributions
of the cases with missing employment displayed in Figure \ref{fig:agemis}. Further, in SIPP-EHC individuals who
report participating in SNAP are twice as likely to have missing income data as those who do not receive SNAP, whereas
in SIPP the rate of missingness for employment status is about the same regardless of SNAP participation. Therefore, we
expect more of those missing employment status in SIPP-EHC actually to be unemployed, and they are evidently imputed as such.

\begin{figure}
\begin{center}
\includegraphics[width=0.55\textwidth]{fig/msipp-empstat}
\end{center}
\vspace{-20pt}
\caption{Percent reporting employment during the
  reference period, with 95\% confidence intervals, for SIPP-EHC and
the  production SIPP subsample.}
\label{fig:empstat}
\end{figure}

Figure \ref{fig:medagesex} displays similar quantities for the median
earnings by age and sex strata. For most strata, accounting for
missing data appears not to have substantial impact on the
comparisons (most estimates and 95\% CIs are similar pre- and
post-imputation).
A notable exception occurs for 35-44 men: the MI estimate for SIPP-EHC is
substantially lower than the complete case estimate and appears more
in line with adjacent strata estimates.
{In this particular cell, there are 122 respondents with observed values, whereas on average there are 172 men in the imputed datasets (these observations were missing either employment status or earnings amounts -- age and sex are completely observed). }%
Evidently, the HCMM-LD\ uses information from other covariates to generate imputations that are more in line with what one would expect, {pulling down the median in this cell to a value more consistent with neighboring estimates}.

\begin{figure}
\begin{center}
\includegraphics[trim={0 0.5cm 0 0},width=0.95\textwidth]{fig/msipp-medagesex}
\end{center}
\vspace{-20pt}
\caption{Median earnings by age and sex in SIPP/SIPP-EHC computed in complete cases and multiply imputed datasets}
\label{fig:medagesex}
\end{figure}

Finally, Figure \ref{fig:snap-home} shows imputed and complete case
estimates of mean home values and SNAP benefits. We focus on means
because these distributions are less skewed than the earnings
distributions. Imputed mean home values are very similar to complete
case estimates, with the differences much smaller than relevant
standard errors.
The mean SNAP amounts are similar in the
imputed and corresponding complete case estimates, but for SIPP-EHC
the MI standard error is much higher than the complete case standard
error. This arises because of the relatively small sample
size; on average across imputations,
there are about 560 respondents in universe for SNAP benefit amounts but only
225 have observed values, so about 60\% of the values are
missing. Moreover, about 25\% of SNAP
recipients are missing earnings data in SIPP-EHC, and earnings are one
of the most important determinants of SNAP benefit amounts (the other
is household size, which is completely observed). Although the rate of
missing amounts in the production SIPP subsample is about the same, SIPP has a lower
rate of missing income data among SNAP recipients (16\% versus
25\%) and a larger sample size (ranging from 893-901 across imputed
datasets). These factors combine to allow for  more precise
imputed estimates of SNAP benefits in the production SIPP subsample.

\begin{figure}

{\centering \includegraphics[trim={0 0.5cm 0 0},width=.45\linewidth]{fig/msipp-homeamt}
\includegraphics[trim={0 0.5cm 0 0},width=.45\linewidth]{fig/msipp-snapamt}

}

\caption{Estimates of mean home value and mean SNAP benefit  in SIPP/SIPP-EHC computed in complete cases and multiply imputed datasets.}
\label{fig:snap-home}
\end{figure}

\subsection{Comparison of SIPP-EHC and production SIPP}

In their complete-case analyses, the Census Bureau researchers reported several
notable differences between the SIPP-EHC and production SIPP data \citep{USCensus2013}.
For variables with fairly low rates of item nonresponse (5\% or
less), of course, accounting for item nonresponse with MAR models is
not likely to alter these conclusions.
Our analyses of the variables with significant
missingness suggest nuanced conclusions about comparability.  In
particular, even after adjusting for item nonresponse, the SIPP-EHC
respondents are more likely to report being employed during the
previous month and also to report lower mean
home values.  Interestingly, Census Bureau researchers \citep{USCensus2013} linked complete cases
to administrative data and found that employment information was generally
more accurate in SIPP-EHC than in SIPP (these records
were not available to us).  Across the two samples, differences in
earnings and mean SNAP benefits tend to be small relative to MI
standard errors, particularly for SNAP benefits where relying on
complete cases appears to underestimate standard errors.

Despite being drawn from the same frame and weighted to the same population, the two data sources do exhibit some
differences among completely observed variables. For example, in
SIPP-EHC,  56.7\% of the householders are female (SD 0.9\%), compared to
60.3\% (SD 0.8\%) in the production SIPP subsample. In SIPP-EHC, the mean householder age is
47.8 (SD 0.34) compared to 50.4 (SD 0.29) in the production SIPP sample, and the quartiles
show a similar difference of about 2 years. A number of factors may
contribute to these differences; one candidate is differential
attrition or unit nonresponse between SIPP and SIPP-EHC, which seems
plausible given the substantial differences in their designs. The Census
Bureau is continuing to examine possible sources for this discrepancy
(personal communication).

\section{Concluding Remarks}\label{sec:conclusion}

The repeated sampling simulation in  Section \ref{sec:sipp-sim} demonstrates that the HCMM-LD\ can serve
as a reliable default multiple imputation engine.  In fact, in the simulation
it often outperformed a default implementation of MICE, which is representative of the most widely used imputation routines.
Of course,
both MICE and the HCMM-LD\ could be modified to incorporate
dataset-specific prior knowledge -- and this is good practice -- but
in our experience many data users rely on default procedures.
We examined many other potential estimands in the simulation study.
For many estimands the difference between default MICE and the HCMM-LD\
are modest, but for others the improvement under
the HCMM-LD\  is substantial.  We suspect that the performance gap to increase as the
sample size grows, because the differences appear to be driven mostly
by misspecification bias. Unlike default MICE, as a nonparametric
Bayesian joint model  the HCMM-LD\ has the potential to increase in
complexity and capture additional features of the data.

We have not performed a systematic evaluation of the
properties of the HCMM-LD\ in large sample, high-dimensional settings;
this is an area for future research.  We are optimistic about its
potential. Computationally, fitting the
HCMM-LD\ reduces to fitting a series of mixture and regression
models. Computational complexity scales roughly linearly with sample size, dominated by computing likelihoods when resampling
cluster indices.%
These steps could be optimized further in our existing implementation.
Increasing the dimension of the
categorical variables is clearly feasible; in an MPMN model \cite{Si2013}
considered simulations with 50 categorical
variables. Increasing the dimension of the continuous variables is more of a strain,
as the computation required grows quickly in
the dimension of the covariance matrices (for example, sampling the $H_i^{(\mathcal{Y})}$ for $1\leq i\leq n$ is $O(n{k^{\mathcal{(Y)}}} q^2)$).

Fitting large
mixtures of multivariate normals is a well-studied problem, however, and specialized, efficient algorithms exist to leverage
parallel computing architectures (e.g. \citet{suchard2010understanding}). These would be
straightforward to adapt to the HCMM-LD. {So too are alternative parameterizations of the component-specific covariance matrices,
such as factor-analytic forms in which $\Sigma_{\hy}= \Lambda_{\hy}\Lambda_{\hy}' + \Omega_\hy$ with $\Omega_\hy$ a diagonal $q\times q$ matrix and $\Lambda_{\hy}$ a $q\times b$ matrix of factor loadings (with $b<< q$). Such models reduce the number of free parameters and regularize the local covariances. They also render $Y_j$ and $Y_{j'}$ conditionally independent given some additional latent variables, simplifying imputation for  $Y$.}

There are a number of interesting directions to extend the HCMM-LD.  In
contexts with fully observed data, it can be advantageous to condition
on fully observed variables, such as design variables, so as not to
spend model fitting capacities on modeling these variables.  Since the
HCMM-LD\ is modular in nature, it is conceptually possible to incorporate
such adaptations.
Similarly, the modular nature suggests that it should be possible to
adapt the model to incorporate other types of variables, such as counts or durations.
Finally, the current model does not account for structural zeros in contingency tables (from impossible
combinations or skip patterns), and linear restrictions
among continuous variables. We expect that it should be possible to
adapt the methods of  \cite{Manrique-Vallier2012,
  Manrique-Vallier2012a} to handle structural zeros and of
\cite{Kim2013} to handle linear constraints.  Adapting these approaches to mixed data
is an active area of research.

redpajama_set_name: RedPajamaArXiv


text:
Western TV shows - #14 New Topic Reply to Topic
chibbi
https://www.msn.com/en-us/tv/gallery/50-best-western-tv-shows-of-all-time/ss-BB15cXca?li=BBnb7Kz#image=38
Making my way to #1 and found our favorite at #14.
I know there have been other list but I do believe they�ve gone up in ranking.
SS Quizmaster Emeritus
The rank-ordering is based on Imdb ratings. It's interesting to note that, of the series of its era, West is beaten out by only three: Zorro, The Rifleman, and Have Gun�Will Travel. Its rating is way ahead of better known "horse operas" like Rawhide, Bonanza, and even Gunsmoke.
And it's really not a western! It's a spy spoof anachronistically set in the 1870s. Alongside its scripts, acting, and production values, I think that's a big reason West still hold up so well. It was never locked into the period because it was never of the period to start with.
Originally posted by ccb
Don�t forget Brisco County Jr.
Actor Bruce Campbell (1993): "In the episode 'Brisco For the Defense,' Brisco uses a slide projector to show a trial jury fingerprint evidence. Professor Wickwire returns many times in the series to assist with technology, including tinkering with motorcycles and rescuing the heroes with a helium-filled zeppelin. Campbell told Starlog magazine, "It's kind of Jules Verne meets The Wild Wild West."
(Note to Mr. Campbell: Verne met West from the very first season, 1965.)
Actor Christian Clemenson (1994): "The similarities between this show and The Wild Wild West, and my character to that show's Artemus Gordon, was an important hook for me. It was one of my favorite shows growing up, and as soon as I saw that Brisco County was based on the same kind of material and attitude as that show, I called my agent and said, 'I'll do anything I have to do to get this.'"
Writer John McNamara said (2002) that he became a "student of TV history" while writing for Brisco, reviewing old episodes of Maverick for inspiration on using humor in the Western genre. He said the writing team felt the television audience was ready for a "trans-genre form," because much of the audience grew up with Lethal Weapon, Star Trek, and The Wild Wild West.
This makes me happy. I'm hoping my daughter will watch it with me. She loves the horse scenes but won't watch a full episode yet. She is only 4. I hate that it was cancelled for violence because todays movies are disturbing in some ways. I don't like a lot of head shots and blood/gore but I love www. <3
Yeah, compaed to current movies and TV shows, WWW was pretty tame!

redpajama_set_name: RedPajamaCommonCrawl


Uploads counting towards download quota?
My usage stats are saying i have gone over my quota (of 500gb) and have used 508gb this month!!
From what I can see it is adding 307gb of downloads to 201gb of uploads, and now my speed has been throttled and is basically unusable as a result of this miscalculation.
Can you please fix it asap!
Re: Uploads counting towards download quota?
Usage allowances on Exetel fibre plans are advertised as anytime data usage.
This means downloads and uploads, both are included towards the usage allowance.
These plans do not have a separate allowance for uploads and that is why the service is now slow as you have exceeded the allowance.
Please reply to the email I sent if you have any further concerns.
Or they could ignore you and leave misleading information on their "Customer help forum".
Up to date information is always available under the recent plan details and it is recommended to check the website plan information.


Army of Rokosz jewels are serious craftsmanship and unique design that we just can't get enough of. This ring is all handmade by Andrea the founder herself. Features a beautiful glossy black rose cut diamond kite and that signature Army Of Rokosz hand carved detail on the yummy yellow band.


Jimmy John's teed themselves up for this one. If you're going to pawn off someone else's joke from a big 'ol company Twitter account as your own, then you better be ready for the internet to call that BS out eventually.
What Good Are QR Codes Anyway?
So many different ways to whiz!


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f^&J NeW Walking' SkirtS Every Kind of material.
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building, Cincinnati, Ohio, and she will!
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DON'T BE TOO HASTY In selecting a Piano.
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South Sixth St. y^UISIC f(k Minn.


Many years have passed since Ronaldinho left FC Barcelona. So far only known one version of the facts and is that Pep Guardiola had decided not to have the Brazilian star for his project at Barca. Years later, it was Dinho himself who has acquitted Guardiola and told the true reason for his departure.
The Brazilian magician has revealed that it was he who made the decision to leave FC Barcelona and not Guardiola who forced him to leave. " I wanted something different and that's why I decided to go out.I still have a lot of friends at FC Barcelona.Pefore I go, Pep Guardiola and I talked.He wanted me to stay, but I wanted to try something different.Pe Pep and I have a great Even though I have a great relationship with his brother because we have known each other for a long time, it would not have changed much if I had been a Guardiola player, " explained Ronaldinho in an interview with FourFour Two.
The Brazilian midfielder links his departure from Barça to Rijkaard and assumes part of the authorship of the style of play that has astonished the world of football in recent years. " When I see FC Barcelona today, I see a lot of the club that we created, the style is the same, possession of the ball and a special player starting from the band, it's not very different ," said Dinho.


text:
Mentors to help nurture students
THE hunt is on to find the best business brains of the future in Coventry and Warwickshire.
The Institute of Directors (IoD) has teamed up with Coventry University for a scheme in which it is hoped the region's business leaders will become mentors to the students.
The Coventry Means Business initiative will also include a competition to find the Best Business Idea, the Best Start-up Business and the Champion Troubleshooter.
The contest is open to the 17,000-strong student body at Coventry University and winners of the categories will receive a financial prize.
Phillip Cornwall, chairman of Coventry and Warwickshire branch of the IoD, said: "We want to persuade hundreds of company directors in the area to become mentors to students.
"They have already gained invaluable knowledge about what it takes to run a successful business and we hope they would be prepared to share this knowledge with the next generation of entrepreneurs."
Stephen Kingswell, chairman of Coventry University Development Committee, said: "It would make an enormous difference to the students to have the practical input from successful business leaders, and businessmen and women will have the opportunity to help shape the entrepreneurs and the economy of the future."
The mentors would be asked to offer a minimum of one year's support.
Sponsors for the awards are also being sought.
To help, phone Stephen Kingswell on 07951 261683 or 024 7688 8589.


This is a detached property located only 5km from the Village of Purchena which has all the amenities.
On the 1st floor; there is a large area of 50m2 it is possible to have 2/3 rooms.
On the 2nd floor; you will find a lounge/diner fitted with a fireplace, and there is a fitted kitchen.
On the third floor; there is a double bedroom and door leading out to a sun terrace, which has beautiful views of the surroundings and mountains.
The land is of 2000m2 it is flat an useful land around the house, good access road too and private parking.
Electricity and water are connected, internet can be connected.


text:
7 Surprising Sights At Geylang Serai
In: Do, Editor's Picks, Explore Singapore, posted: Jul 8, 2016
As Hari Raya Puasa celebrations begin, here are the best places to be at in Geylang Serai
Known as the heart of Singapore's Malay community, Geylang Serai is an exciting hub of activity, especially now that Hari Raya Puasa celebrations are underway. Its name was derived from the Malay words kilang (meaning "factory") and serai ("lemongrass"), referring to the lemongrass plantations that used to flourish here in the 1800s.
Geylang Serai was also home to many other plantations such as coconut, rubber and tapioca, leading to its other name, Kampong Ubi (or "tapioca village").
If you're in the area for the occasion, or happen to pop by this culturally rich part of town, here are the top places to explore for a greater appreciation of the neighbourhood.
The Geylang Serai Market sells mostly Malay and Middle-Eastern products. (Photo: Jeff Masilungan / Flickr)
1. Geylang Serai Market
Located just five minutes from Paya Lebar MRT, Geylang Serai Market is a two-storey Malay-style building housing a trove of Malay and Middle-Eastern products such as spices, traditional medicine, batiks, cosmetics and more. You may even come across exotic products such as snakes and turtle eggs here.
After shopping up a storm, you may be feeling slightly peckish. Trot over to the hawker centre beside the wet market, where you can feast on hearty Malay fare like nasi padang (rice with ingredients) and irresistible goreng pisang (fried banana fritters).
If you're here for a leisurely exploration, visit the market during off-peak hours and avoid the peak period of 6 a.m. till 9.30 a.m. If you're up to testing out your haggling skills, you can try approaching the shopkeepers toward the end of the day.
Geylang Serai Market, 1 Geylang Serai
A version of this article appeared in the print edition of Weekender, Issue 156, July 8 - July 21, 2016, with the headline 'Sedap! Sights & sounds at Geylang Serai'.
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King David is brought to you by THTC founder and CEO, Gav Lawson. If there ever was a face that signifies what we stand for at THTC, it would be Sir David Attenborough's. Through many years of active research and dedicated reporting on our 'Goliath' planet's flora and fauna, we celebrate Sir David's work with a homage to the great man by immortalising him on fabric.
Coming to you this winter on hemp and organic cotton, we salute the King of environmental documentation, King David. If there is anyone that knows about climate change, it is Sir David, and we have posted a video below entitled 'The truth about climate change'.


text:
DriveRuntime: 62+ mins, 17 songs
Runtime: 62+ mins, 17 songs
Playlist Creator: Antony Nunez
Last updated: Aug 21st, 2018
1 A NIGHT 2 REMEBER feat. SHALAMAR (feat. WeGotHipHop.com) Daz Dillinger3:32
2 Let Me Clear My Throat (Old School Reunion Remix '96) (feat. Doug E Fresh & Biz Markie) DJ Kool Herc4:51
3 RAW (BIG DADDY KANE) (feat. EPMD, KRS ONE, BIG DADDY KANE, KOOL G RAP & ERIC B AND RAKIM) Shawn Djashawn Aiken2:49
4 Big Daddy Kane - Rap Summary (Lean On Me) (feat. Big Daddy Kane, Kid N Play, Eric B, Rakim, LL Cool J & MC Lyte) 704 DJs0:00
5 Shook Ones Pt. 2 (feat. Mobb Deep) (feat. Snoop Dogg, Ice Cube, Dr. Dre, Eazy-E, N.W.A., Run-D.M.C., Coolio, Mobb Deep & Cypress Hill) Old School5:25
6 No Diggity [DV Remix] (feat. Dr.Dre & Queen Pen) Blackstreet5:26
7 Don't stop me now QUEEN3:37
8 All of me --- Slow 80 Bpm to Fast 128 Bpm ( DjProWings Mashup Edit ) John Legend4:49
9 Shalamar-A Night To Remember (feat. WeGotHipHop.com) DJ Triple Exe - Retro Gold 53:08
10 10 Shannon - Let The Music Play (12'' Dub Version) MUSICAS6:06
Antony Nunez
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Old School Check Yo Self (Remix) (feat. Ice Cube)
Feat. Snoop Dogg, Ice Cube, Dr. Dre, Eazy-E, N.W.A., Run-D.M.C., Coolio, Mobb Deep & Cypress Hill
Album: Old School
Added on: Sep 20th, 2015 by Jirka Corleone


PETA » POP! goes The Vegan.
Last night's episode of The Colbert Report included a segment on PETA's $1 million reward for the successful development and marketing of in vitro meat.
Though The Colbert Report is usually animal-friendly in its coverage, I was more than a little disappointed by this particular segment. Throughout the report, Stephen appears to be mocking the idea of in vitro meat as both disgusting and infeasible, rather than mocking, say, meat-eaters who might think cultured meat is disgusting and infeasible – when, in reality, the "meat" on their plates is cobbled together from the parts of many previously living animals, crowded together in filthy factory farms and pumped full of antibiotics, then slaughtered, sometimes while fully conscious, by the billions, and that such a system is environmentally destructive and unsustainable. Instead, the ick factor is reserved for the "bloody egg yolk," without any sort of follow-up "gotcha!" moment aimed at the meat-eating culture Stephen introduces the segment with. Or am I missing something? Thoughts?
On the plus side, the Mr. noticed a "chill" come over the crowd when a slaughterhouse worker was shown "shaving" (for lack of a better word) the top layer of skin (fat?) from a raw, hanging animal corpse. Perhaps Stephen managed to convert a new vegetarian?
This entry was posted on Wednesday, March 18th, 2009 at 5:09 pm and is filed under Television. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.
…for making the consumption of "land fish" socially acceptable!
Video links: January 15, 2009: Tip/Wag – Monkey on the Lam and January 15, 2009: Spay and Neuter Your Pets.
This entry was posted on Saturday, January 17th, 2009 at 6:02 pm and is filed under Television. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.
I've been meaning to blog about a recent episode of Life for weeks now. If you're not familiar with the show, it's a kind of cop drama, in which individual cases are presented against the backdrop of a conspiracy-theory story arc which spans the series. Think The X-Files, Alias, Lost or The Mentalist – if you enjoy any of these, you'll probably *heart* Life, too.
Dr. Auerbach was a scientist who was testing cancer drugs on animals. So his death naturally occurs in the lab and on the window is written, "animal testing is murder." Something not so natural about his death: He was frozen to death because some one switched his oxygen tank with a liquid nitrogen tank. But who could have done it? Maybe it was the group, BAT [Ban Animal Torture], that has sent Dr. Auerbach death threats?
According to the group's leader, Betsy, they wouldn't hurt any soul, even one like Dr. Auerbach's. She seems sweet enough. She even tells the other member to be quiet when he says it's good the doctor is dead. So if it wasn't her, maybe it was the assistant who seems too concerned with the results of the test. Or maybe the janitor? Or the company's owner? Hmm. I can't decide, and neither can Crews [Damian Lewis] and Reese [Sarah Shahi] so they do a little more digging and come up with…Betsy, the leader of Ban and the good doctor's former assistant who left because they were having an affair. Say what?
I know, it's a crazy little twist but it turns out that Betsy's real name is Deborah and she and Dr. Auerbach never stopped their affair. And while it seems she has the perfect motive of conflicted emotions, she also has a videotaped alibi. So then Crews and Reese move on to the janitor, who originally said he saw Betsy at the lab that day. Turns out the janitor is stealing pills from the study and selling them. Or so it looks when he gives the box of pills to a woman on a park bench in return for an envelope full of…pictures? When Crews and Reese dig a little deeper they find the janitor's son has cancer and the pills have been working for him and the woman is his ex-wife. I guess he has a good motive, too. And more importantly, he confesses to the murder. But something isn't right. Along with the dead doctor, there were lots of dead lab rats. The only dead rats, though, were rats with red tags so why would only those rats be dead and who would want to kill them?
With the help of then now cleared ex-assistant, Crews and Reese learn that the red tagged rats were the control rats and you would want those to be gone if you didn't want other people to know the experiment was a failure. And who would want that? Yup, the new assistant. Turns out she knew the janitor was stealing pills and blackmailed him. But he wasn't such a moron that he didn't have evidence damning her. He had a formula she wrote computing how much liquid nitrogen it would take to kill a man the doctor's size. So the dedicated assistant killed the doctor after all. She had spent seven years working with him and now her career would be over because the drug was a failure. It was only helping the janitor's son because he had an extremely rare form of cancer. It wouldn't work on the mainstream cases. Guess that liar is busted.
Unlike many other cop dramas (the Law & Order franchise, if I recall, has featured its fair share of guilty, stereotyped animal rights extremists), Life doesn't simply pin the crime on the "obvious suspects" and move on. Rather than get swept up in the Green Scare, Detectives Crews and Reese follow the evidence…which leads them away from the "bad"/"misanthropic" animal rights activists and toward the "good"/"altruistic" cancer researchers.
This entry was posted on Wednesday, November 12th, 2008 at 7:44 pm and is filed under Television. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.
I thought it went swimmingly, with nary a boo to be heard. I mean, I know Dr. Colbert's crowd is fairly liberal, but even most libs poo-poo vegetarianism.
This entry was posted on Saturday, March 1st, 2008 at 7:55 pm and is filed under Television. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.


Olympus UK E-System User Group > Show your photos > Exhibitions, stock photos, professional work > Which Photos SELL ? for YOU ?
View Full Version : Which Photos SELL ? for YOU ?
"Why would a customer want to buy one of your prints? and what need in the customer's mind are you satisfying?"
Derek asks two very valid questions! We go to Craft Fairs to sell and complain no one is buying - THIS is why so many small business ventures fail ! No thought and Planning ! Know your Customer ? Know your Product ? and know Your Market/Competition?
You can sell Ice to Eskimo's - I forget why !
So What do you sell ? and to who ? and How ?
My Market is generally the Ladies about the Villages here - who want a nice card for their friends - blank for special occasions go very well - and many buy then in packs of 10's as notelets ! This is the "elders", a generation who do not email, but write :D and many still use a Founatin Pen :eek: I love my Shaeffer; Waterman and Cross Fountain Pens & Nibs - I use different coloured inks too (for my Caligraphy - Quotations & Poems in the main).
I have a few (? hundreds) of Equine friends ... always keen to have another Great shot of their horses and dogs and sometimes children - they buy Flowers and Equine shots and a few Landscapes ... I do a few "Team Chase events" and a few "BSJA Shows" and a few "BHS Dressage shows" (mainly because of my own past competative interest and to meet up with old mates ... and ... BTW sell a few cards & Prints !
I do not attempt to gain revenue - at one time I did a lot of photography for a charity, the dog training classes, Puppy Party, out and about training sessions. Special events, visits of Clebs etc. I had one invite from a puppy parent to do a wedding - I declined, better, to disappoint in advance than post delivery. However I get asked to cover neighbours parties and weddings as the "pap" photographer, booze and food provided as per the other guests and a day or twos work creating a web site and slide show on DVD etc.
Had quite a few published in various papers, Sky Magazine - just think, 9 million copies of several of my pictures went out to line the bottom of the cat litter tray.
Currently on the cover of a couple of books in Japan and one of the Med countries.
Back to the subject - I think that an extension of your honesty box principle could be used. except that you get some exceptional postcards of the local area and then seed them in the local shops alongside the standard postcards and see if they sell better than the existing range. This is an expense led activity ie you provide the first stock for free. Perhaps you have a small advert on the back of the card offering a large version for real money.
Can you beat the current offerings for postcards of Winchester? if so try the shops in town and not limit yourself to the local village. The Scottish pro who posts on here has success with postcards of his local landscapes as well as his larger prints.
It depends if you mean licensing to publishers or selling prints.
Although the Red Fox was also published in a field guide.
I thought the duck picture was drawn by some artist.wrong.
I still on occasions do this for family or friends.
Strangely enough although I do not market my images I have sold a few off my website and to some unusual buyers that have been a bit like selling ice to Eskimo's except I did not have to sell them.
I was approached by a American history book Publisher wanting a image of mine for a book called Nurses through the ages.
Now this request coming from the land of American Civil War!
Paul, I just LURVE the Welsh Lamb in a field of Daffodils - for NZ :D ROFL lots !
The Nurses, well the confederate and yankee flags are in shot - and they have blue skies over there in USA! However, that grass is very RARE int he USA ! ... but they would not notice that !
I went to a talk a couple of days ago with a PowerPoint slide show, and some of the photos were not that great (DoF Problems). The speaker said she'd bought some off the internet, and I'm afraid I wasn't impressed with those either.
I have better ones, a lot of people here have superb ones. I don't know how to sell mine and the one time I tried through Flickr (was it from a thread here? I think so) it was a no. I think I lack confidence, especially when I see what people on here can produce, so I've never approached sotock photo things except that once, which was an obliwque approach anyway.
Yet I suspect this speaker would have paid a few pence to use my photos... or yours... because they're better.
If I had the self-confidence that's what I'd try.
Maybe we should have a stock thread on here. Maybe we could have an Olympus Group Stock Gallery?
I sell stock still as I have mentioned in another thread, the issue is the "pence" thing.
A lot of people aren't happy with that level of value being placed on their work.
I can easily see why the lamb and the ACW pics were published, I bet it wasn't pence either for that usage.


DOWNLOAD RECEIPT FOR NIOS D.EL.ED COUNCELLING Free Online Courses|TEJ TUBE. projects program Only secret you need to know to solve all Business Case Studies (with Example. Nios Deled examination form fill up. Nios deled case study [sba] इस तरह लिखिए | Maintenance of school class records का उत्तर फॉर्मेट, Deled Lesson Plan EVS पर्यावरण अध्ययन पाठ योजना लिखिए This page contains a detailed analysis of the backlinks of hindihelpguru.com. Find out which pages link to the website and find the most important links.
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https://www.theintelligencer.com/news/article/Dewey-8217-s-Pizza-introduces-new-seasonal-pizza-13742781.php
Dewey's Pizza introduces new seasonal pizza alongside Mike's Hot Honey
Bre Booker, bre.booker@edwpub.net
Updated 1:10 pm CDT, Monday, April 8, 2019
Dewey's Pizza launched a brand-new seasonal pizza, Sgt Peppers on Monday.
Photo Courtesy Of Dewey's Pizza.
EDWARDSVILLE — Dewey's Pizza announced that it is launching a brand-new seasonal pizza, Sgt. Peppers. Local St. Louis and tri-state locations will be partnering with Mike's Hot Honey for the first time to give pizza lovers and music enthusiasts a tasty and colorful take on a new pizza, which began Monday.
The inspiration behind Dewey's Pizza's Sgt Peppers comes from one of the greatest rock albums of all time: Sgt. Peppers Lonely Hearts Club Band. It was a concept album that created the idea of flowing one song track into the next. As a tribute to this ground-breaking idea and the iconic album artwork, Dewey's Pizza was inspired to create a medley of red bell, Anaheim, fresh jalapeno and banana peppers, chopped pepperoni and crushed red pepper to provide a seamless experience of all things pepper with every bite. The Sgt. Peppers pizza is then topped off with Mike's Hot Honey, a chili pepper infused with honey, which provides the pizza with the perfect amount of sweet to balance the peppers' heat.
"This new pizza is one of the most unique pies we've ever created for our Dewey's Pizza guests," said Ryan Laker, Culinary Innovation Manager at Dewey's Pizza. "We are excited and grateful to be partnered with Mike's Hot Honey to add that extra 'wow' factor to our new seasonal Sgt. Peppers."
The pizza will be spicy, but all of the peppers shouldn't stop guests from trying a piece.
"It's going to be a little spicier, it's not going to be too overwhelming; it's a pretty mellow spice," Edwardsville Dewey's Manager Rachel Levin told an Intelligencer reporter.
Dewey's Pizza is always seeking the best way to bring quality pizza to their customers and when the opportunity with Mike's Hot Honey arouse they knew it would add quality to their Sgt. Peppers pie, according to Levin.
"I know they've taken a lot of time to incorporate what we want for our guests," Levin said. "They always bring good quality with their products so, knowing that, we really wanted to team up with them to see what we could bring our guests."
From April 8 through May 4, Dewey's Pizza and Mike's Hot Honey will be celebrating the partnership and release of this new seasonal pizza with giveaways on social media and much more in all 25 of Dewey's Pizza locations."We're thrilled to be working with Dewey's on their seasonal pizza, and love seeing what happens when we put Mike's Hot Honey in the hands of creative pizza people," said Matt Beaton, CEO of Mike's Hot Honey. "This pizza pie is equally beautiful and delicious."
Dewey's Pizza has 7 St. Louis and tri-state store locations, including: Ellisville, Kirkwood, St. Charles, U-City, Webster Groves, Edwardsville and O'Fallon. Sgt Peppers pizza will also be available at all 25 locations nationwide. To find a Dewey's location near you visit deweyspizza.com.


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