I'm quite confused about interpreting the results from the lme4 package. When looking through this webpage and google, it seems like more people are generally confused. I cannot find a clear overview on what to do with all the output, so I hope this thread can function as a general overview for more people.

I'll use my data as an example: I have a 4 (between:groups)x 2 (within:time) design. I am looking for an interaction effect on reaction times of an attentional control task (e.g. stroop task). Since I have an unbalanced design (16, 19, 14 and 17 obs per group) after removing outliers, I wanted to use the lmer function to run a mixed anova (or mixed model now) in R.

I run the following command:

options(contrasts = c("contr.sum", "contr.poly"))

lmer_mixed_ANOVA <- lmer(control_out ~time*Groups + (1|ID),

data=data_RT_control)print(Anova(lmer_mixed_ANOVA,type=3))

print(anova(lmer_mixed_ANOVA,type=3))

print(summary(lmer_mixed_ANOVA))

and I get this as output:

` [1] "data_RT_control" Analysis of Deviance Table (Type III Wald chisquare tests) Response: control_out Chisq Df Pr(>Chisq) (Intercept) 291.1728 1 < 2.2e-16 *** time 9.3639 1 0.002213 ** Groups 2.1204 3 0.547791 time:Groups 6.5060 3 0.089427 . --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Analysis of Variance Table of type III with Satterthwaite approximation for degrees of freedom Sum Sq Mean Sq NumDF DenDF F.value Pr(>F) time 8164.2 8164.2 1 58.039 9.3639 0.003348 ** Groups 1848.8 616.3 3 58.980 0.7068 0.551774 time:Groups 5672.4 1890.8 3 57.995 2.1687 0.101448 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Linear mixed model fit by REML t-tests use Satterthwaite approximations to degrees of freedom ['lmerMod'] Formula: control_out ~ time * Groups + (1 | ID) Data: all_dataframes[[i]] REML criterion at convergence: 1301 Scaled residuals: Min 1Q Median 3Q Max -2.4262 -0.5228 -0.1374 0.5249 2.3927 Random effects: Groups Name Variance Std.Dev. ID (Intercept) 262.2 16.19 Residual 871.9 29.53 Number of obs: 136, groups: ID, 70 Fixed effects: Estimate Std. Error df t value Pr(>|t|) (Intercept) 54.778 3.210 59.020 17.064 < 2e-16 *** time1 -7.819 2.555 58.040 -3.060 0.00335 ** Groups1 -3.448 4.399 58.990 -0.784 0.43626 Groups2 2.560 2.732 59.150 0.937 0.35263 Groups3 -1.519 1.830 58.900 -0.830 0.40978 time1:Groups1 -5.170 3.501 58.020 -1.477 0.14512 time1:Groups2 -3.987 2.176 58.160 -1.832 0.07200 . time1:Groups3 -1.476 1.456 57.920 -1.014 0.31478 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Correlation of Fixed Effects: (Intr) time1 Grops1 Grops2 Grops3 tm1:G1 tm1:G2 time1 -0.031 Groups1 -0.035 0.021 Groups2 0.087 -0.004 0.027 Groups3 -0.022 0.002 0.020 -0.051 time1:Grps1 0.021 -0.044 -0.030 -0.016 -0.012 time1:Grps2 -0.004 0.087 -0.016 -0.033 0.002 0.034 time1:Grps3 0.002 -0.023 -0.012 0.002 -0.029 0.026 -0.051 `

This chunk of output is really overwhelming! Different tables give different p-values. Is there an overview, or would someone be willing to create an overview of how to interpret these outcomes step by step.

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#### Best Answer

I assume that the order of your output matches the order of the code. The output object is lmer_mixed_ANOVA

The **Anova** function is a function from the car package. It appears to be doing calculations on deviances, not fixed effects t-tests or z-tests in an ANOVA table. The **anova** function is a method for output object from the lmer function. This table is comparable to SAS Type III sum of squares because of the type option.

The **summary** function applied to the output object gives the scaled residuals, the random effects, and the estimates of each fixed effect level, and the correlations of these effects. It sets the intercept to Group0, time0. 'time1' is the difference between the two time points, at Group 0. The three estimates called Group'n' are the difference between each Group and Group 0 at time 0. The following interaction terms are estimates at each Group level and time 1. The t-tests after the estimates test if these differences are equal to 0.

Yes, mixed models in R is confusing. I prefer commercial software for ease of use.

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