[R] Growth Curves with lmer

[Michael Scharkow]

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