I am fitting a general linear model using glmer from lme4 on data with a binary outcome (0 and 1). This is choice trial data with approximately 140 choices per participant. The model I run is as follows:
library(lme4)
m1 <- glmer(stay ~ prevpoints * same * prevrewdiff * Age_c + (1| participant), data = my_Data, family = binomial)
Stay and same are binomial, where stay takes values 0 or 1 and same takes values -1 and 1. Prevpoints and prevrewdiff are continuous between 0 and 1. Age_c is a centered age variable that is continuous between -2.07 and +1.88.
Below is the summary from the model:
>summary(m1)
Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
Family: binomial ( logit )
Formula: stay ~ prevpoints * same * prevrewdiff * Age_c + (1 | subnr)
Data: Stay_kids_P6_age
AIC BIC logLik deviance df.resid
12919.4 13041.0 -6442.7 12885.4 9439
Scaled residuals:
Min 1Q Median 3Q Max
-2.2668 -1.0186 0.6574 0.9415 1.6634
Random effects:
Groups Name Variance Std.Dev.
subnr (Intercept) 0.1138 0.3373
Number of obs: 9456, groups: subnr, 85
Fixed effects:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -0.111493 0.081965 -1.360 0.17375
prevpoints 0.464269 0.130130 3.568 0.00036 ***
same 0.074867 0.072461 1.033 0.30151
prevrewdiff 0.073866 0.157075 0.470 0.63817
Age_c 0.008594 0.050718 0.169 0.86545
prevpoints:same -0.066014 0.128513 -0.514 0.60748
prevpoints:prevrewdiff -0.134402 0.259995 -0.517 0.60520
same:prevrewdiff -0.039067 0.156090 -0.250 0.80237
prevpoints:Age_c 0.046862 0.081110 0.578 0.56343
same:Age_c -0.005506 0.044802 -0.123 0.90219
prevrewdiff:Age_c -0.231429 0.098529 -2.349 0.01883 *
prevpoints:same:prevrewdiff 0.120424 0.258361 0.466 0.64114
prevpoints:same:Age_c -0.011628 0.080023 -0.145 0.88447
prevpoints:prevrewdiff:Age_c 0.249957 0.163381 1.530 0.12604
same:prevrewdiff:Age_c -0.041121 0.097907 -0.420 0.67449
prevpoints:same:prevrewdiff:Age_c 0.166707 0.162442 1.026 0.30477
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
So it seems that prevpoints and prevrewdiff*age are the only significant effects.
While, when I run anova(m1) I see:
anova(m1)
Analysis of Variance Table
npar Sum Sq Mean Sq F value
prevpoints 1 30.7102 30.7102 30.7102
same 1 5.4894 5.4894 5.4894
prevrewdiff 1 0.0171 0.0171 0.0171
Age_c 1 0.0092 0.0092 0.0092
prevpoints:same 1 0.0222 0.0222 0.0222
prevpoints:prevrewdiff 1 0.3641 0.3641 0.3641
same:prevrewdiff 1 0.0280 0.0280 0.0280
prevpoints:Age_c 1 10.3298 10.3298 10.3298
same:Age_c 1 0.0784 0.0784 0.0784
prevrewdiff:Age_c 1 3.8111 3.8111 3.8111
prevpoints:same:prevrewdiff 1 0.2806 0.2806 0.2806
prevpoints:same:Age_c 1 1.6501 1.6501 1.6501
prevpoints:prevrewdiff:Age_c 1 2.3021 2.3021 2.3021
same:prevrewdiff:Age_c 1 0.6115 0.6115 0.6115
prevpoints:same:prevrewdiff:Age_c 1 1.0601 1.0601 1.0601
Where there is a large F value for prevpoints * Age_c.
In sum I have two questions:
- Previously, I don't remember models run with the lme4 package to give p-values, and I've read discussions online about how the p-values should ideally not be used. However, now they seem to be given by default. Has this changed recently and should p-values now be more trusted as output?
- I don't understand why the F-value is so large when I run the anova, but that this then does not translate to a significant estimate for the prevpoints*Age_c estimate. Would anybody know what's going on here?
