[R-lang] Random slopes in LME

[Zhenguang Cai]

Hi all,

I have a question concerning random slopes in mixed effects modeling. 
So I ran a structural priming experiment with a 4-level variable (prime 
type, A, B, D and D). The dependent variable is response construction 
(DO dative vs. PO dative).  The following is a summary of the experiment 
results.

Prime		A	B	C	D
DOs		85	24	38	59
POs		82	144	128	109
% of DOs	.51	.14	.23	.35

I am interested in whether different prime types induced different 
priming, e.g., whether A led to more DO responses than B, C or D. 
Initially, I ran LME analyses with random intercepts only. For instance, 
I did the following to see whether there was a main effect of prime type.

fit.0 = lmer(Response~1+(1|Subject)+(1|Item), family=binomial)
fit.p = lmer(Response~Prime+(1|Subject)+(1|Item), family=binomial)
anova (fit.0, fit.p)

Then, I did pairwise comparison by changing the reference level for 
Prime, e.g.,

fit.p = lmer(Response~relevel(Prime,ref="B")+(1|Subject)+(1|Item),
family=binomial)

It seems that all the levels differed from each other. In particular, 
the comparison between C and D results in Estimate = -1.02, SE = .32, Z
= -3.21, p < .01.

But it seems I have to consider whether the slope for Prime differs 
across subjects or item (at least this is a requirement from JML). So 
the following is the way I considered whether a random slope should be 
included in a model. I wonder whether I did the correct thing. I first 
determined whether subject random slope should be included by comparing 
the following two models.

fit.p = lmer(Response~Prime+(1|Subject)+(1|Item), family=binomial)
fit.ps = lmer(Response~Prime+(Prime+1|Subject)+(1|Item), family=binomial)
anova (fit.p, fit.ps)

I did the same thing about item random slopes.

fit.p = lmer(Response~Prime+(1|Subject)+(1|Item), family=binomial)
fit.pi = lmer(Response~Prime+(1|Subject)+(Prime+1|Item), family=binomial)
anova (fit.p, fit.pi)

The subject random slope had a significant effect, so I included it in 
the final model (e.g., fit.ps). But pairwise comparison returned 
something that is different from my initial analyses (when random slope 
was not considered). That is, the comparison between C and D became only 
marginally significant (Estimate = -.85, SE = .47, z = -1.79, p = .07). 
It is a bit strange because the 9% difference between B and C turned out 
to be significant, but the 12% difference between C and D was not.

Or did I do anything wrong in the analyses?

Thanks,

Garry