Summary of Linear Mixed Regression Models as HTML Table

Daniel Lüdecke

2017-10-19

This document shows examples for using the sjt.lmer() function of the sjPlot package.

# load required packages
library(sjPlot)
library(sjmisc)
library(sjlabelled)
library(lme4)

Linear mixed models summaries as HTML table

The sjt.lmer() function prints summaries of linear mixed models (fitted with the lmer() function of the lme4-package) as nicely formatted html-tables.

Before starting, sample data is loaded and sample models are fitted:

# load sample data
data(efc)
# prepare grouping variables
efc$grp = as.factor(efc$e15relat)
levels(x = efc$grp) <- get_labels(efc$e15relat)
efc$care.level <- rec(efc$n4pstu, rec = "0=0;1=1;2=2;3:4=4", val.labels = c("none", "I", "II", "III"))

# data frame for fitted model
mydf <- data.frame(
  neg_c_7 = efc$neg_c_7,
  sex = to_factor(efc$c161sex),
  c12hour = efc$c12hour,
  barthel = efc$barthtot,
  education = to_factor(efc$c172code),
  grp = efc$grp,
  carelevel = to_factor(efc$care.level)
  )

# fit sample models
fit1 <- lmer(neg_c_7 ~ sex + c12hour + barthel + (1 | grp), data = mydf)
fit2 <- lmer(neg_c_7 ~ sex + c12hour + education + barthel + (1 | grp), data = mydf)
fit3 <- lmer(neg_c_7 ~ sex + c12hour + education + barthel +
              (1 | grp) + (1 | carelevel), data = mydf)

The simplest way of producing the table output is by passing the fitted models as parameter. By default, estimates (B), confidence intervals (CI) and p-values (p) are reported. The models are named Model 1 and Model 2.

The resulting table is divided into three parts:

  1. Fixed parts - the model’s fixed effects coefficients, including confidence intervals and p-values.
  2. Random parts - the model’s group count (amount of random intercepts) as well as the Intra-Class-Correlation-Coefficient ICC and information on the random effect variances (within-group, between-group etc.)
  3. Summary - Observations, AIC etc.
sjt.lmer(fit1, fit2)
    Negative impact with 7 items   Negative impact with 7 items
    B CI p   B CI p
Fixed Parts
(Intercept)   14.14 13.15 – 15.12 <.001   13.75 12.63 – 14.87 <.001
carer’s gender (Female)   0.48 -0.07 – 1.03 .091   0.67 0.10 – 1.25 .023
average number of hours of care per week   0.00 -0.00 – 0.01 .238   0.00 -0.00 – 0.01 .218
Total score BARTHEL INDEX   -0.05 -0.06 – -0.04 <.001   -0.05 -0.06 – -0.04 <.001
carer’s level of education (intermediate level of education)       0.19 -0.43 – 0.80 .550
carer’s level of education (high level of education)       0.80 0.03 – 1.58 .045
Random Parts
σ2   12.189   12.320
τ00, grp   0.279   0.267
Ngrp   8   8
ICCgrp   0.022   0.021
Observations   872   815
R2 / Ω02   .185 / .185   .193 / .193

Custom labels

You can specify the ‘model’ label via depvar.labels parameter:

sjt.lmer(fit1, fit2,
         depvar.labels = c("Negative Impact", "Negative Impact"))
    Negative Impact   Negative Impact
    B CI p   B CI p
Fixed Parts
(Intercept)   14.14 13.15 – 15.12 <.001   13.75 12.63 – 14.87 <.001
carer’s gender (Female)   0.48 -0.07 – 1.03 .091   0.67 0.10 – 1.25 .023
average number of hours of care per week   0.00 -0.00 – 0.01 .238   0.00 -0.00 – 0.01 .218
Total score BARTHEL INDEX   -0.05 -0.06 – -0.04 <.001   -0.05 -0.06 – -0.04 <.001
carer’s level of education (intermediate level of education)       0.19 -0.43 – 0.80 .550
carer’s level of education (high level of education)       0.80 0.03 – 1.58 .045
Random Parts
σ2   12.189   12.320
τ00, grp   0.279   0.267
Ngrp   8   8
ICCgrp   0.022   0.021
Observations   872   815
R2 / Ω02   .185 / .185   .193 / .193

More custom labels

Here is an example how to change the other labels. Note that show.header makes the two labels on top and top left corner appear in the table.

sjt.lmer(fit1, fit2, show.header = TRUE, string.est = "Estimate", 
         string.ci = "Conf. Int.", string.p = "p-value",
         string.dv = "Response", string.pred = "Coefficients",
         string.interc = "Konstante",
         depvar.labels = c("Negative Impact", "Negative Impact"))
Coefficients Response
  Negative Impact   Negative Impact
    Estimate Conf. Int. p-value   Estimate Conf. Int. p-value
Fixed Parts
Konstante   14.14 13.15 – 15.12 <.001   13.75 12.63 – 14.87 <.001
carer’s gender (Female)   0.48 -0.07 – 1.03 .091   0.67 0.10 – 1.25 .023
average number of hours of care per week   0.00 -0.00 – 0.01 .238   0.00 -0.00 – 0.01 .218
Total score BARTHEL INDEX   -0.05 -0.06 – -0.04 <.001   -0.05 -0.06 – -0.04 <.001
carer’s level of education (intermediate level of education)       0.19 -0.43 – 0.80 .550
carer’s level of education (high level of education)       0.80 0.03 – 1.58 .045
Random Parts
σ2   12.189   12.320
τ00, grp   0.279   0.267
Ngrp   8   8
ICCgrp   0.022   0.021
Observations   872   815
R2 / Ω02   .185 / .185   .193 / .193

Changing summary style and content

You can change the table style with specific parameters, e.g. to include CI into the same table cell as the estimates, print asterisks instead of numeric p-values etc.

sjt.lmer(fit1, fit2,
         separate.ci.col = FALSE, # ci in same cell as estimates
         show.std = TRUE,         # also show standardized beta values
         p.numeric = FALSE,       # "*" instead of numeric values
         show.re.var = FALSE,     # no random effect variances
         show.aic = TRUE,         # AIC
         show.dev = FALSE,        # no deviance
         show.r2 = FALSE)          # no Pseudo-R2
#> Warning: Some models were fit with REML. To get meaningful AIC values for
#> comparison, refit models with ML (`REML = FALSE`).
    Negative impact with 7 items   Negative impact with 7 items
    B (CI) std. Beta (CI)   B (CI) std. Beta (CI)
Fixed Parts
(Intercept)   14.14
(13.15 – 15.12) ***
    13.75
(12.63 – 14.87) ***
 
carer’s gender (Female)   0.48
(-0.07 – 1.03) 
0.05
(-0.01 – 0.11)
  0.67
(0.10 – 1.25) *
0.07
(0.01 – 0.14)
average number of hours of care per week   0.00
(-0.00 – 0.01) 
0.04
(-0.03 – 0.12)
  0.00
(-0.00 – 0.01) 
0.05
(-0.03 – 0.12)
Total score BARTHEL INDEX   -0.05
(-0.06 – -0.04) ***
-0.37
(-0.44 – -0.30)
  -0.05
(-0.06 – -0.04) ***
-0.37
(-0.44 – -0.30)
carer’s level of education (intermediate level of education)       0.19
(-0.43 – 0.80) 
0.02
(-0.05 – 0.10)
carer’s level of education (high level of education)       0.80
(0.03 – 1.58) *
0.08
(0.00 – 0.16)
Random Parts
Ngrp   8   8
ICCgrp   0.022   0.021
Observations   872   815
AIC   4691.393   4397.996
Notes * p<.05   ** p<.01   *** p<.001

Custom variable labels

In the above example, the original variable labels are long and not much pretty. You can change variable labels either with sjmisc::set_label(), which will affect all future plots and tables, or pass own labels via pred.labels.

sjt.lmer(fit1, fit2, pred.labels = c("Carer's Sex",
         "Hours of Care", "Elder's Dependency",
         "Mid Educational Level", "High Educational Level"))
    Negative impact with 7 items   Negative impact with 7 items
    B CI p   B CI p
Fixed Parts
(Intercept)   14.14 13.15 – 15.12 <.001   13.75 12.63 – 14.87 <.001
Carer’s Sex   0.48 -0.07 – 1.03 .091   0.67 0.10 – 1.25 .023
Hours of Care   0.00 -0.00 – 0.01 .238   0.00 -0.00 – 0.01 .218
Elder’s Dependency   -0.05 -0.06 – -0.04 <.001   -0.05 -0.06 – -0.04 <.001
Mid Educational Level       0.19 -0.43 – 0.80 .550
High Educational Level       0.80 0.03 – 1.58 .045
Random Parts
σ2   12.189   12.320
τ00, grp   0.279   0.267
Ngrp   8   8
ICCgrp   0.022   0.021
Observations   872   815
R2 / Ω02   .185 / .185   .193 / .193

Grouping predictors

Categorical variables with more than two levels can be grouped in the table output. Grouping means, that a row with the variable label is inserted before these variables, and a value label for each category (i.e. factor level) is printed with a small margin.

sjt.lmer(fit3, fit2, fit1, group.pred = TRUE)
    Negative impact with 7 items   Negative impact with 7 items   Negative impact with 7 items
    B CI p   B CI p   B CI p
Fixed Parts
(Intercept)   13.76 12.63 – 14.88 <.001   13.75 12.63 – 14.87 <.001   14.14 13.15 – 15.12 <.001
carer’s gender (Female)   0.65 0.08 – 1.22 .029   0.67 0.10 – 1.25 .023   0.48 -0.07 – 1.03 .091
average number of hours of care per week   0.00 -0.00 – 0.01 .208   0.00 -0.00 – 0.01 .218   0.00 -0.00 – 0.01 .238
carer’s level of education
intermediate level of education   0.16 -0.46 – 0.79 .606   0.19 -0.43 – 0.80 .550    
high level of education   0.79 0.01 – 1.57 .052   0.80 0.03 – 1.58 .045    
Total score BARTHEL INDEX   -0.05 -0.06 – -0.04 <.001   -0.05 -0.06 – -0.04 <.001   -0.05 -0.06 – -0.04 <.001
Random Parts
σ2   12.413   12.320   12.189
τ00, grp   0.264   0.267   0.279
τ00, carelevel   0.000        
Ngrp   8   8   8
Ncarelevel   4        
ICCgrp   0.021   0.021   0.022
ICCcarelevel   0.000        
Observations   807   815   872
R2 / Ω02   .190 / .190   .193 / .193   .185 / .185

Note that in the above example, the order of fitted model was changed. This is sometimes necessary, because grouping categorical predictors does not always work properly when multiple models with different amount and order of predictors are printed in one table.

Models with different random intercepts

When models have different random intercepts, the sjt.lmer() function tries to detect these information from each model. In the Random parts section of the table, information on multiple grouping levels and ICC’s are printed then.

sjt.lmer(fit1, fit2, fit3)
    Negative impact with 7 items   Negative impact with 7 items   Negative impact with 7 items
    B CI p   B CI p   B CI p
Fixed Parts
(Intercept)   14.14 13.15 – 15.12 <.001   13.75 12.63 – 14.87 <.001   13.76 12.63 – 14.88 <.001
carer’s gender (Female)   0.48 -0.07 – 1.03 .091   0.67 0.10 – 1.25 .023   0.65 0.08 – 1.22 .029
average number of hours of care per week   0.00 -0.00 – 0.01 .238   0.00 -0.00 – 0.01 .218   0.00 -0.00 – 0.01 .208
Total score BARTHEL INDEX   -0.05 -0.06 – -0.04 <.001   -0.05 -0.06 – -0.04 <.001   -0.05 -0.06 – -0.04 <.001
carer’s level of education (intermediate level of education)       0.19 -0.43 – 0.80 .550   0.16 -0.46 – 0.79 .606
carer’s level of education (high level of education)       0.80 0.03 – 1.58 .045   0.79 0.01 – 1.57 .052
Random Parts
σ2   12.189   12.320   12.413
τ00, grp   0.279   0.267   0.264
τ00, carelevel           0.000
Ngrp   8   8   8
Ncarelevel           4
ICCgrp   0.022   0.021   0.021
ICCcarelevel           0.000
Observations   872   815   807
R2 / Ω02   .185 / .185   .193 / .193   .190 / .190

Note that in certain cases, depending on the order of fitted models with several random intercepts, the group label might be incorrect.

More space bewteen model columns

Especially when fitting and summarizing some more models, it might help to increase the distance between the columns that separate the models. This can be done by tweaking the css.separatorcol style-sheet:

sjt.lmer(fit1, fit2, fit3, 
         CSS = list(css.separatorcol = 'padding-right:1.5em; padding-left:1.5em;'),
         show.re.var = FALSE,
         show.icc = FALSE,
         show.r2 = FALSE)
    Negative impact with 7 items   Negative impact with 7 items   Negative impact with 7 items
    B CI p   B CI p   B CI p
Fixed Parts
(Intercept)   14.14 13.15 – 15.12 <.001   13.75 12.63 – 14.87 <.001   13.76 12.63 – 14.88 <.001
carer’s gender (Female)   0.48 -0.07 – 1.03 .091   0.67 0.10 – 1.25 .023   0.65 0.08 – 1.22 .029
average number of hours of care per week   0.00 -0.00 – 0.01 .238   0.00 -0.00 – 0.01 .218   0.00 -0.00 – 0.01 .208
Total score BARTHEL INDEX   -0.05 -0.06 – -0.04 <.001   -0.05 -0.06 – -0.04 <.001   -0.05 -0.06 – -0.04 <.001
carer’s level of education (intermediate level of education)       0.19 -0.43 – 0.80 .550   0.16 -0.46 – 0.79 .606
carer’s level of education (high level of education)       0.80 0.03 – 1.58 .045   0.79 0.01 – 1.57 .052
Random Parts
Ngrp   8   8   8
Ncarelevel           4
Observations   872   815   807

Removing estimates from the output

With remove.estmates, specific estimates can be removed from the table output. This may make sense in case you have stepwise regression models and only want to compare the varying predictors but not the controls. remove.estmates either accepts the row indices of the rows of the table output that should be removed, or the coefficient’s names.

When using numeric indices, the estimates’ index number relates to the same order as coef(fit).

Example 1: Complete table output

Here you have the complete table output. This helps you identify the row index numbers. Especially when you have multiple models with different predictors, the estimate’s position in the last model may differ from this estimate’s position in the table output.

sjt.lmer(fit1, fit2, fit3,
         show.re.var = FALSE,
         show.icc = FALSE)
    Negative impact with 7 items   Negative impact with 7 items   Negative impact with 7 items
    B CI p   B CI p   B CI p
Fixed Parts
(Intercept)   14.14 13.15 – 15.12 <.001   13.75 12.63 – 14.87 <.001   13.76 12.63 – 14.88 <.001
carer’s gender (Female)   0.48 -0.07 – 1.03 .091   0.67 0.10 – 1.25 .023   0.65 0.08 – 1.22 .029
average number of hours of care per week   0.00 -0.00 – 0.01 .238   0.00 -0.00 – 0.01 .218   0.00 -0.00 – 0.01 .208
Total score BARTHEL INDEX   -0.05 -0.06 – -0.04 <.001   -0.05 -0.06 – -0.04 <.001   -0.05 -0.06 – -0.04 <.001
carer’s level of education (intermediate level of education)       0.19 -0.43 – 0.80 .550   0.16 -0.46 – 0.79 .606
carer’s level of education (high level of education)       0.80 0.03 – 1.58 .045   0.79 0.01 – 1.57 .052
Random Parts
Ngrp   8   8   8
Ncarelevel           4
Observations   872   815   807
R2 / Ω02   .185 / .185   .193 / .193   .190 / .190

Example 2: Remove first coefficient (after intercept)

sjt.lmer(fit1, fit2, fit3,
         remove.estimates = 2,
         show.re.var = FALSE,
         show.icc = FALSE)
    Negative impact with 7 items   Negative impact with 7 items   Negative impact with 7 items
    B CI p   B CI p   B CI p
Fixed Parts
(Intercept)   14.14 13.15 – 15.12 <.001   13.75 12.63 – 14.87 <.001   13.76 12.63 – 14.88 <.001
average number of hours of care per week   0.00 -0.00 – 0.01 .238   0.00 -0.00 – 0.01 .218   0.00 -0.00 – 0.01 .208
Total score BARTHEL INDEX   -0.05 -0.06 – -0.04 <.001   -0.05 -0.06 – -0.04 <.001   -0.05 -0.06 – -0.04 <.001
carer’s level of education (intermediate level of education)    –    0.19 -0.43 – 0.80 .550   0.16 -0.46 – 0.79 .606
carer’s level of education (high level of education)    –    0.80 0.03 – 1.58 .045   0.79 0.01 – 1.57 .052
Random Parts
Ngrp   8   8   8
Ncarelevel           4
Observations   872   815   807
R2 / Ω02   .185 / .185   .193 / .193   .190 / .190

Example 3: Remove hours of care and sex

sjt.lmer(fit1, fit2, fit3,
         remove.estimates = c("c12hour", "sex2"),
         show.re.var = FALSE,
         show.icc = FALSE)
    Negative impact with 7 items   Negative impact with 7 items   Negative impact with 7 items
    B CI p   B CI p   B CI p
Fixed Parts
(Intercept)   14.14 13.15 – 15.12 <.001   13.75 12.63 – 14.87 <.001   13.76 12.63 – 14.88 <.001
Total score BARTHEL INDEX   -0.05 -0.06 – -0.04 <.001   -0.05 -0.06 – -0.04 <.001   -0.05 -0.06 – -0.04 <.001
carer’s level of education (intermediate level of education)    –    0.19 -0.43 – 0.80 .550   0.16 -0.46 – 0.79 .606
carer’s level of education (high level of education)    –    0.80 0.03 – 1.58 .045   0.79 0.01 – 1.57 .052
Random Parts
Ngrp   8   8   8
Ncarelevel           4
Observations   872   815   807
R2 / Ω02   .185 / .185   .193 / .193   .190 / .190