[R-sig-ME] Compare goodness of fit between models

[David Duffy]

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.

-- 
| David Duffy (MBBS PhD)                                         ,-_|\
| email: davidD at qimr.edu.au  ph: INT+61+7+3362-0217 fax: -0101  /     *
| Epidemiology Unit, Queensland Institute of Medical Research   \_,-._/
| 300 Herston Rd, Brisbane, Queensland 4029, Australia  GPG 4D0B994A v