R help - Aug 2010 - Growth Curves with lmer

Dear all,

I have some growth curve data from an experiment that I try to fit using
lm and lmer. The curves describe the growth of classification accuracy
with the amount of training data t, so basically

y ~ 0 + t (there is no intercept because y=0 at t0)

Since the growth is somewhat nonlinear *and* in order to estimate the
treatment effect on the growth curve, the final model is

y ~ 0 + t + t.squared + t:treat + t,squared:treat

this yields:
       t   t.sq   t:treat   t.sq:treat
   1.08   -0.007    0.39   -0.0060

This fits the data fairly well, but I have replicated data for 12
different classifiers. First, I tried 12 separate regressions which
yielded results with different positive values for t and t:treat.

Finally, I tried to estimate a varying intercept model using lmer

lmer(y ~ 0+t+t.squared+t:treat+t,squared:treat+(0+t+t.squared+t:treat
+t,squared:treat | classifier)

The fixed effects are similar to the pooled regression, but most of the
random effects for t and t:treat are implausible (negative). What's
wrong with the lmer model? Did I misspecify something?

Greetings,
Michael

Classification accuracy is an improper scoring rule, and one of the 
problems with it is that the proportional classified correctly can be 
quite good even if the model uses no predictors.  [Hence omitting the 
intercept is also potentially problematic.]

Frank E Harrell Jr   Professor and Chairman        School of Medicine
                      Department of Biostatistics   Vanderbilt University

On Wed, 11 Aug 2010, Michael Scharkow wrote:
> Dear all,
>
> I have some growth curve data from an experiment that I try to fit using
> lm and lmer. The curves describe the growth of classification accuracy
> with the amount of training data t, so basically
>
> y ~ 0 + t (there is no intercept because y=0 at t0)
>
> Since the growth is somewhat nonlinear *and* in order to estimate the
> treatment effect on the growth curve, the final model is
>
> y ~ 0 + t + t.squared + t:treat + t,squared:treat
>
> this yields:
>       t   t.sq   t:treat   t.sq:treat
>   1.08   -0.007    0.39   -0.0060
>
> This fits the data fairly well, but I have replicated data for 12
> different classifiers. First, I tried 12 separate regressions which
> yielded results with different positive values for t and t:treat.
>
> Finally, I tried to estimate a varying intercept model using lmer
>
> lmer(y ~ 0+t+t.squared+t:treat+t,squared:treat+(0+t+t.squared+t:treat
> +t,squared:treat | classifier)
>
> The fixed effects are similar to the pooled regression, but most of the
> random effects for t and t:treat are implausible (negative). What's
> wrong with the lmer model? Did I misspecify something?
>
> Greetings,
> Michael
>
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