SPSS Linear Mixed Model repeated covariance type

Question

I need your help with regards to specifying repeated covariance type in SPSS.

I am trying to build a Linear Mixed Model in SPSS with the subject being 'borough' and repeated variable being YEAR . My dependent variable is the number of people claiming housing benefit, per year (for 7 years overall), for each borough. All my covariates (fixed effects) represent a value for a tax year. Examples of my covariates are: population, unemployment rate, mean rent, median house price to median earnings ratio. I've tried setting different covariance types and the results do differ significantly, so I guess it is important to set the correct one. I've tried researching, how to determine the repeated covariance type but I've been unsuccessful. This is the only guidance I've found https://www.ibm.com/support/knowled...ariance_structures.html#covariance_structures however, as I am not a statistician (but a sociologist) these descriptions mean nothing to me and sound like a foreign language.

The covariance types options are:

• Ante-Dependence:First Order
• AR1
• AR1 Heterogenous
• ARMA
• Compound Symmetry
• Compound Symmetry: Correlation Metric
• Compound Symmetry: Heterogenous
• Diagonal
• Factor Analytic: First Order
• Factor Analytic: First Order, Heterogeneous
• Huynh-Feldt
• Scaled Identity
• Toeplitz
• Toeplitz: Heterogenous
• Unstructured
• Unstructured:Correlations

I would be grateful for your help!

Answer 1

This question is really difficult to answer in a simple way. I don't think the comment above is actually germane, as I don't see in the question any reference to inclusion of random effects on a RANDOM subcommand, only repeated measures on a REPEATED subcommand.

There are references out there that discuss using likelihood-ratio tests to compare the same fixed-effects model with different covariance structures to compare simpler to more complex covariance structures. This requires that the structures compared be nested (the more complex structure must contain all the parameters in the simpler one). A similar empirical approach is to compare information criteria to assess whether the additional covariance parameters are worth the degrees of freedom they consume, and this doesn't require the structures to be nested.

To consider which types of structures to really look at, you need to think about what kind of temporal dependence you would expect to find in your dependent variable. Would it get less as time goes on? Then something like an autoregressive structure might make sense. Would it be pretty much the same across all time points? Then a compound symmetric version might be reasonable. I'm afraid there's no way for anyone else to give a simple recommendation here.