# How do you interpret linear mixed effect model results?

I made a linear mixed effect model using the mtcars datset with the following parameters:

IV: mtcars$am, DV: mtcars$disp, Controlling for mtcars$gear, mtcars$carb

Here is the model results itself:

Linear mixed model fit by maximum likelihood  ['lmerMod']
Formula: disp ~ am + (1 | gear) + (1 | carb)
Data: mtcars

AIC      BIC   logLik deviance df.resid
375.7    383.0   -182.8    365.7       27

Scaled residuals:
Min       1Q   Median       3Q      Max
-2.44542 -0.63575 -0.06279  0.51475  1.70509

Random effects:
Groups   Name        Variance Std.Dev.
carb     (Intercept) 4032     63.50
gear     (Intercept) 6960     83.43
Residual             3062     55.34
Number of obs: 32, groups:  carb, 6; gear, 3

Fixed effects:
Estimate Std. Error t value
(Intercept)   218.83      59.66   3.668
mtcars$am -12.32 34.51 -0.357 Correlation of Fixed Effects: (Intr) mtcars$am -0.325


Here is the p value analysis results:

 Analysis of Deviance Table (Type II Wald chisquare tests)

Response: disp

Chisq Df Pr(>Chisq)

mtcars$am 0.1275 1 0.7211  According to these results, this model was not significant (χ² = 0.1275, p = 0.7211). When controling for mtcars$gear and mtcars$carb, when mtcars$am == 0 the mtcars$disp estimate is 218.83 and when mtcars$am == 1 the mtcars$disp estimate is 206.51 [218.83 + (-12.32) = 206.51], but these differences are not significantly different than one another (mtcars$am == 0 v. mtcars$am == 1). Is my interpretation of the results correct? Thanks ahead of time. Here is the code I used to make the data:  # linear mixed effect model - IV: mtcars$$am, DV: mtcars$$disp, Controlling for mtcars$$gear, mtcars$$carb ## dataset of interest mtcars ### colnames(mtcars) colnames(mtcars) ### unique values for variable of interest unique(mtcars$$am) unique(mtcars$$disp) unique(mtcars$$gear) unique(mtcars$$carb) ## gives descriptives for mtcars$$disp overall, mtcars__am_is_0$$disp, and mtcars__am_is_1$disp

library(psych)

#### for all data, mtcars$disp ##### loads tidyverse package library(tidyverse) ##### nrow(mtcars) nrow(mtcars) ##### description of describe(mtcars$disp)

#### for mtcars__am_is_1$disp ##### creates mtcars__am_is_1 object mtcars__am_is_1 <- mtcars %>% filter(mtcars$$am == 1) mtcars__am_is_1 <- data.frame(mtcars__am_is_1) mtcars__am_is_1 unique(mtcars__am_is_1$$am) nrow(mtcars__am_is_1) ##### description of describe(mtcars__am_is_1$disp)

#### for mtcars__am_is_0$disp ##### creates mtcars__am_is_0 object mtcars__am_is_0 <- mtcars %>% filter(mtcars$$am == 0) mtcars__am_is_0 <- data.frame(mtcars__am_is_0) mtcars__am_is_0 unique(mtcars__am_is_0$$am) nrow(mtcars__am_is_0) ##### description of describe(mtcars__am_is_0$disp)

## linear mixed effect model - IV: mtcars$$am, DV: mtcars$$disp, Controlling for mtcars$$gear, mtcars$$carb

### The code below loads the needed packages for the test
library(car)
library(MASS)
library(lme4)

### IV: mtcars$$am, DV: mtcars$$disp, Controlling for mtcars$$gear, mtcars$$carb
names(mtcars)
unique(mtcars$$am) unique(mtcars$$disp)
unique(mtcars$$gear) unique(mtcars$$carb)
lmem__IV_am__DV__disp__Controlling_for_gear_and_carb <- lmer(disp ~ am + (1 | gear) + (1 | carb), data = mtcars, REML = FALSE)
lmem__IV_am__DV__disp__Controlling_for_gear_and_carb__summary <- summary(lmem__IV_am__DV__disp__Controlling_for_gear_and_carb)
lmem__IV_am__DV__disp__Controlling_for_gear_and_carb__summary

### The code below uses anova to generate p values for the lmer code above
lmem__IV_am__DV__disp__Controlling_for_gear_and_carb__significance <- Anova(lmem__IV_am__DV__disp__Controlling_for_gear_and_carb)
lmem__IV_am__DV__disp__Controlling_for_gear_and_carb__significance



The model you have fitted specifies carb and gear as grouping factors for random intercepts. These have only 6 and 3 levels respectively. It might be possible to get away with 6, but 3 is too few to get a reasonable estimate for it's variance. gear should definitely be a fixed effect, not random.