One of four related functions for mixed effects analyses (based on lmer and as_lmerModLmerTest) to get a linear model for downstream steps, or an ANOVA table.
mixed_model
mixed_anova
mixed_model_slopes
mixed_anova_slopes.
mixed_model(data, Y_value, Fixed_Factor, Random_Factor, ...)a data table object, e.g. data.frame or tibble.
name of column containing quantitative (dependent) variable, provided within "quotes".
name(s) of categorical fixed factors (independent variables) provided as a vector if more than one or within "quotes".
name(s) of random factors to allow random intercepts; to be provided as a vector when more than one or within "quotes".
any additional arguments to pass on to lmer if required.
This function returns an S4 object of class "lmerModLmerTest".
These functions require a data table, one dependent variable (Y_value), one or more independent variables (Fixed_Factor), and at least one random factor (Random_Factor). These should match names of variables in the long-format data table exactly.
Outputs of mixed_model and mixed_model_slopes can be used for post-hoc comparisons with posthoc_Pairwise, posthoc_Levelwise, posthoc_vsRef, posthoc_Trends_Pairwise, posthoc_Trends_Levelwise and posthoc_Trends_vsRefor with emmeans.
More than one fixed factors can be provided as a vector (e.g. c("A", "B")). A full model with interaction term is fitted.
This means when Y_value = Y, Fixed_factor = c("A", "B"), Random_factor = "R" are entered as arguments, these are passed on as Y ~ A*B + (1|R) (which is equivalent to Y ~ A + B + A:B + (1|R)).
In mixed_model_slopes and mixed_anova_slopes, the following kind of formula is used: Y ~ A*B + (S|R) (which is equivalent to Y ~ A + B + A:B + (S|R)).
In this experimental implementation, random slopes and intercepts are fitted ((Slopes_Factor|Random_Factor)). Only one term each is allowed for Slopes_Factor and Random_Factor.
#one fixed factor and random factor
mixed_model(data = data_doubling_time,
Y_value = "Doubling_time",
Fixed_Factor = "Student",
Random_Factor = "Experiment")
#> boundary (singular) fit: see help('isSingular')
#> Linear mixed model fit by REML ['lmerModLmerTest']
#> Formula: Doubling_time ~ Student + (1 | Experiment)
#> Data: data_doubling_time
#> REML criterion at convergence: 95.2499
#> Random effects:
#> Groups Name Std.Dev.
#> Experiment (Intercept) 0.000
#> Residual 1.989
#> Number of obs: 30, groups: Experiment, 3
#> Fixed Effects:
#> (Intercept) StudentB StudentC StudentD StudentE StudentF
#> 19.9619 -0.3713 -0.5929 -1.1728 -0.6286 0.7416
#> StudentG StudentH StudentI StudentJ
#> 0.4885 -0.8083 0.6775 1.2115
#> optimizer (nloptwrap) convergence code: 0 (OK) ; 0 optimizer warnings; 1 lme4 warnings
#two fixed factors as a vector, one random factor
mixed_model(data = data_cholesterol,
Y_value = "Cholesterol",
Fixed_Factor = c("Treatment", "Hospital"),
Random_Factor = "Subject")
#> Linear mixed model fit by REML ['lmerModLmerTest']
#> Formula: Cholesterol ~ Treatment * Hospital + (1 | Subject)
#> Data: data_cholesterol
#> REML criterion at convergence: 376.5107
#> Random effects:
#> Groups Name Std.Dev.
#> Subject (Intercept) 51.756
#> Residual 6.524
#> Number of obs: 50, groups: Subject, 25
#> Fixed Effects:
#> (Intercept) TreatmentBefore_drug
#> 147.011 26.165
#> HospitalHosp_b HospitalHosp_c
#> -4.587 -42.004
#> HospitalHosp_d HospitalHosp_e
#> 15.770 15.432
#> TreatmentBefore_drug:HospitalHosp_b TreatmentBefore_drug:HospitalHosp_c
#> -8.075 -7.001
#> TreatmentBefore_drug:HospitalHosp_d TreatmentBefore_drug:HospitalHosp_e
#> -27.202 -25.803
#save model
model <- mixed_model(data = data_doubling_time,
Y_value = "Doubling_time",
Fixed_Factor = "Student",
Random_Factor = "Experiment")
#> boundary (singular) fit: see help('isSingular')
#get model summary
summary(model)
#> Linear mixed model fit by REML. t-tests use Satterthwaite's method [
#> lmerModLmerTest]
#> Formula: Doubling_time ~ Student + (1 | Experiment)
#> Data: data_doubling_time
#>
#> REML criterion at convergence: 95.2
#>
#> Scaled residuals:
#> Min 1Q Median 3Q Max
#> -1.94563 -0.40680 -0.04097 0.42601 1.45893
#>
#> Random effects:
#> Groups Name Variance Std.Dev.
#> Experiment (Intercept) 0.000 0.000
#> Residual 3.956 1.989
#> Number of obs: 30, groups: Experiment, 3
#>
#> Fixed effects:
#> Estimate Std. Error df t value Pr(>|t|)
#> (Intercept) 19.9619 1.1484 20.0000 17.383 1.54e-13 ***
#> StudentB -0.3713 1.6241 20.0000 -0.229 0.821
#> StudentC -0.5929 1.6241 20.0000 -0.365 0.719
#> StudentD -1.1728 1.6241 20.0000 -0.722 0.479
#> StudentE -0.6286 1.6241 20.0000 -0.387 0.703
#> StudentF 0.7416 1.6241 20.0000 0.457 0.653
#> StudentG 0.4885 1.6241 20.0000 0.301 0.767
#> StudentH -0.8083 1.6241 20.0000 -0.498 0.624
#> StudentI 0.6775 1.6241 20.0000 0.417 0.681
#> StudentJ 1.2115 1.6241 20.0000 0.746 0.464
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Correlation of Fixed Effects:
#> (Intr) StdntB StdntC StdntD StdntE StdntF StdntG StdntH StdntI
#> StudentB -0.707
#> StudentC -0.707 0.500
#> StudentD -0.707 0.500 0.500
#> StudentE -0.707 0.500 0.500 0.500
#> StudentF -0.707 0.500 0.500 0.500 0.500
#> StudentG -0.707 0.500 0.500 0.500 0.500 0.500
#> StudentH -0.707 0.500 0.500 0.500 0.500 0.500 0.500
#> StudentI -0.707 0.500 0.500 0.500 0.500 0.500 0.500 0.500
#> StudentJ -0.707 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500
#> optimizer (nloptwrap) convergence code: 0 (OK)
#> boundary (singular) fit: see help('isSingular')
#>