Compare goodness of fit between models
On Wed, 20 Jul 2011, Sverre Stausland wrote:
Dear mixed-models helpers, say I have a study where I try to predict people's response to how happy they are on a 1-5 scale. The data frame has the dependent variable "Response" (1-5) and a random effect for "Subject". I fit a model with the fixed effects "Height" and "Income". I also fit a model with the fixed effects "Weight" and "Hours of sleep". In this case where the dependent variable, subjects, and the number of observations are the same in the two models, am I justified to directly compare the goodness-of-fit values for the two models?
You can, but you can't draw any substantive conclusions ;) If A and B are equally important independent causes of Y, then I might expect Y~A and Y~B submodels to have equal goodness-of-fit values. If A causes B, ditto.
Please note that this is a hypothetical example. I know that I in this case should just fit a model with all four fixed effects. In the real case I have, that is not an option.
In a graphical or SEM framework, you are able to incorporate external information about Weight and Height into your model. Just 2c, David.
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