[R-sig-ME] Comparison of conditional AIC (cAIC) from two or more LMMs

[BELLO YUSUF]

a) Can I compare the AICs obtained from lm and lmer modeled from the same
data set?

b) I want to see if models (lmer) from the correlations (similarities) of
observations obtained from classifications by means of cluster analysis
performed better than models from correlations of observations obtained
from natural (initial) clustering.

I have a crime data of 300 local divisions (level 1 units) unevenly
distributed across 40 districts (level 2 units). I call it Data1. I decided
to use cluster analysis to reclassify the level 1 units to obtain 40 new
clusters of similar crime concentrations, and so new cluster membership was
obtained differently from Data1. I call the second classification as Data2.
Note that the same level 1 units and size were maintained in the two data
sets, but with differences in cluster membership. I used lmer to model the
two data sets.

·         Data 1 & 2 have 40 clusters each, same level 1 size, same level 1
units and same df. residuals, but with differences in cluster membership.

1.       If the conditional AIC (cAIC) for model1 {Data1) is 1032.4 and the
cAIC for model2 {Data2)  is 872.1, can I say model2 better fit the data
than model1?

2.       I reclassify the initial data set and got 30 new optimal clusters
by similarity and named it Data3,

·         such that Data3 has 30 clusters and Data 1 & 2 have 40 clusters
each;

·         All have the same level 1 sizes, same level 1 units and same df.
residuals but with differences in cluster membership. If the cAIC is 903.7
from model3, can I say model2 is better than model3?

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