Examples of correlated error structures GenStat allows the Random Model to be defined with a reasonable selection of correlations structures. The * indicates models that StATS has used relatively frequently. Model Commonly used for: independent, normally distributed errors in a regression or ANOVA Identity* with constant variance essentially the correlated structure for a multi-strata design uniform* (RCB, split-plot etc) diagonal* for any design with changing variance autoregressive (AR1 or AR2) serially correlated errors in time AR* series/repeated measures; spatial models in field trials equivalent to AR1 but allows unequally spaced time points; spatial models in field trials with unequally spaced coordinates time series/repeated measures data where no assumption is made unstructured* about the correlations over time; MANOVA data time series/repeated measures data allowing changing variance, plus: order = 1 reproduces sample correlations for neighbouring time antedependence* points; order = 2 reproduces sample correlations for first and second neighbouring time points; involves fewer parameters than unstructured a mixture of autoregressive and moving average serially correlated ARMA errors in time series/repeated measures boundedlinear correlations decrease linearly in proportion to ratio of distance apart correlations decay spherically with distance, more common in soil spherical science equally close points have the same correlation, the order determines banded correlation how many are non-zero Correlation structure is in terms of a factor analysis model using FA & FAequal fewer parameters than unstructured; more common in plant breeding Fixed correlation matrix specified by user moving average serially correlated errors in time series/repeated MA measures serially correlated errors in time series/repeated measures in the circular correlation changes with distance in a way that depends on the sin-1 function; linearvariance correlations decay linear with distance, more common in soil science What follows is a selection of examples that use some of the correlation models above. The first half of this manual described the structure. Identity The examples are mostly illustrated in an earlier manual available on the page on . Resources Example 1 structure: randomised block models uniform –
Examples of correlated error structures GenStat allows the Random Model to be defined with a reasonable selection of correlations structures. The * indicates models that StATS has used relatively frequently. Model Commonly used for: Identity* independent, normally distributed errors in a regression or ANOVA with constant variance uniform* essentially the correlated structure for a multi-strata design (RCB, split-plot etc) diagonal* for any design with changing variance AR* autoregressive (AR1 or AR2) serially correlated errors in time series/repeated measures; spatial models in field trials equivalent to AR1 but allows unequally spaced time points; spatial models in field trials with unequally spaced coordinates unstructured* time series/repeated measures data where no assumption is made about the correlations over time; MANOVA data antedependence* time series/repeated measures data allowing changing variance, plus: order = 1 reproduces sample correlations for neighbouring time points; order = 2 reproduces sample correlations for first and second neighbouring time points; involves fewer parameters than unstructured ARMA a mixture of autoregressive and moving average serially correlated errors in time series/repeated measures boundedlinear correlations decrease linearly in proportion to ratio of distance apart spherical correlations decay spherically with distance, more common in soil science banded correlation equally close points have the same correlation, the order determines how many are non-zero FA & FAequal Correlation structure is in terms of a factor analysis model using fewer parameters than unstructured; more common in plant breeding Fixed correlation matrix specified by user MA moving average serially correlated errors in time series/repeated measures circular serially correlated errors in time series/repeated measures in the correlation changes with distance in a way that depends on the sin-1 function; linearvariance correlations decay linear with distance, more common in soil science What follows is a selection of examples that use some of the correlation models above. The first half of this manual described the Identity structure. The examples are mostly illustrated in an earlier manual available on the Resources page on . Example 1 – uniform structure: randomised block models
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