The Improbable Nature of the  Implied Correlation Matrix  from Spatial Regression Models
<|begin_of_text|><|start_header_id|>system<|end_header_id|> You are a research archivist expert in dataset metadata. Answer the question truthfully.  <|eot_id|><|start_header_id|>user<|end_header_id|> Here is the Description of a dataset. Description:'Spatial lag dependence in a regression model is similar to the inclusion of a serially autoregressive term for the dependent variable in a time-series context. However, unlike in the time-series model, the implied covariance structure matrix from the spatial autoregressive model can have a very counterintuitive and improbable structure. A single value of spatial autocorrelation parameter can imply a large band of values of pair-wise correlations among different observations of the dependent variable, when the weight matrix for the spatial model is specified exogenously. This is illustrated using cigarette sales data (1963–1992) of 46 US states. It can be seen that that two 'close' neighbours can have very low implied correlations compared to distant neighbours when the weighting scheme is the first-order contiguity matrix. However, i' . Please return only a json list of at most 3 Keywords corresponding to the Description:.<|eot_id|><|start_header_id|>assistant<|end_header_id|> {"Answer" : ["patial Dependence, Variance-Covariance matrix, Implied Correlation  Structure, Weight Matrix."]} <|eot_id|>
 Here is the Description of a dataset. Description:'Spatial lag dependence in a regression model is similar to the inclusion of a serially autoregressive term for the dependent variable in a time-series context. However, unlike in the time-series model, the implied covariance structure matrix from the spatial autoregressive model can have a very counterintuitive and improbable structure. A single value of spatial autocorrelation parameter can imply a large band of values of pair-wise correlations among different observations of the dependent variable, when the weight matrix for the spatial model is specified exogenously. This is illustrated using cigarette sales data (1963–1992) of 46 US states. It can be seen that that two 'close' neighbours can have very low implied correlations compared to distant neighbours when the weighting scheme is the first-order contiguity matrix. However, i' . Please return only a json list of at most 3 Keywords corresponding to the Description:.
Spatial lag dependence in a regression model is similar to the inclusion of a serially autoregressive term for the dependent variable in a time-series context. However, unlike in the time-series model, the implied covariance structure matrix from the spatial autoregressive model can have a very counterintuitive and improbable structure. A single value of spatial autocorrelation parameter can imply a large band of values of pair-wise correlations among different observations of the dependent variable, when the weight matrix for the spatial model is specified exogenously. This is illustrated using cigarette sales data (1963–1992) of 46 US states. It can be seen that that two 'close' neighbours can have very low implied correlations compared to distant neighbours when the weighting scheme is the first-order contiguity matrix. However, i
patial Dependence, Variance-Covariance matrix, Implied Correlation  Structure, Weight Matrix. 