I ran a generalized linear mixed model using lmer in R, and I'm struggling how to interpret the result. The response variable is a result of 25 consecutive binary choices. The point where I'm stuck is:
- What does it mean that the correlation btw random effects are +/-1?
- What does it mean that the random components have 0, or nearly 0 variance? In my result, the slope of age_group (avgIMI) and age_group.1 (sv_hard) are nearly 0. Does it just mean that there is no random effect related to that term?
- I coded the age group as 0 and 1 (young/old each). Then are the random effect group age_group.1 and .2 young and olde groups, respectively? Then what is the age_group? Is it something like aggregated random effect over two age groups?
- Why does the random effect of the interaction term only appears in age_group.2?
- What is "scaled residuals"?
- How do I interpret the correlation btw fixed effects?
Here is the result of my model
Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) [glmerMod] Family: binomial ( logit ) Formula: cbind(round(hard_ratio * 25), 25 - round(hard_ratio * 25)) ~ avgIMI + (avgIMI | age_group) + sv_hard + (sv_hard | age_group) + sv_hard * avgIMI + (sv_hard * avgIMI | age_group) Data: data Control: glmer_ctrl AIC BIC logLik deviance df.resid 990.7 1039.7 -475.3 950.7 66 Scaled residuals: Min 1Q Median 3Q Max -4.9388 -1.9589 0.1634 1.8168 4.7085 Random effects: Groups Name Variance Std.Dev. Corr age_group (Intercept) 5.269e-10 2.295e-05 avgIMI 3.513e-11 5.927e-06 -1.00 age_group.1 (Intercept) 0.000e+00 0.000e+00 sv_hard 4.318e-13 6.571e-07 NaN age_group.2 (Intercept) 2.743e+00 1.656e+00 sv_hard 2.052e-01 4.530e-01 -1.00 avgIMI 2.007e-01 4.480e-01 -1.00 1.00 sv_hard:avgIMI 3.239e-02 1.800e-01 1.00 -1.00 -1.00 Number of obs: 86, groups: age_group, 2 Fixed effects: Estimate Std. Error z value Pr(>|z|) (Intercept) -2.1585 1.2181 -1.772 0.07638 . avgIMI 0.5951 0.3281 1.814 0.06967 . sv_hard 1.3092 0.4911 2.666 0.00767 ** avgIMI:sv_hard -0.4379 0.1600 -2.737 0.00620 ** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Correlation of Fixed Effects: (Intr) avgIMI sv_hrd avgIMI -0.999 sv_hard -0.634 0.654 avgIMI:sv_h 0.784 -0.801 -0.971
It seems I didn't deliver enough details about my problems. The data was collected from 26 younger (age 20~30) and 23 older (age 65~88) participants. They conducted an experimental task in which they repeatedly choose between easy and difficult levels (25 times in total). The response variable is the ratio of the difficult task was chosen. And I also collected participants' task motivation(avgIMI) and their rating of task difficulty(sv_hard). My research question is that whether there is an age group difference in the relationship among the choice ratio, avgIMI and sv_hard. My conjecture was that individuals in the same group (younger/older) is not independent and the data is hierarchical. That's why I tried mixed effect model. I'm confused about whether it's appropriate to go for it.