Summary of Mixed Models as HTML Table

This vignette shows examples for using tab_model() to create HTML tables for mixed models. Basically, tab_model() behaves in a very similar way for mixed models as for other, simple regression models, as shown in this vignette.

# load required packages
library(sjPlot)
library(lme4)
data("sleepstudy")
data("efc")
efc$cluster <- as.factor(efc$e15relat)

Mixed models summaries as HTML table

Unlike tables for non-mixed models, tab_models() adds additional information on the random effects to the table output for mixed models. You can hide these information with show.icc = FALSE and show.re.var = FALSE. Furthermore, the R-squared values are marginal and conditional R-squared statistics, based on Nakagawa et al. 2017.

m1 <- lmer(neg_c_7 ~ c160age + c161sex + e42dep + (1 | cluster), data = efc)
m2 <- lmer(Reaction ~ Days + (1 + Days | Subject), data = sleepstudy)

tab_model(m1, m2)

	Negative impact with 7 items			Reaction
Predictors	Estimates	CI	p	Estimates	CI	p
(Intercept)	6.55	4.86 – 8.23	<0.001	251.41	237.94 – 264.87	<0.001
carer’ age	-0.00	-0.03 – 0.02	0.802
carer’s gender	0.47	-0.08 – 1.02	0.094
elder’s dependency	1.45	1.19 – 1.71	<0.001
Days				10.47	7.42 – 13.52	<0.001
Random Effects
σ²	12.61			654.94
τ₀₀	0.50 _cluster			612.10 _Subject
τ₁₁				35.07 _Subject.Days
ρ₀₁				0.07 _Subject
ICC	0.04			0.72
N	8 _cluster			18 _Subject
Observations	888			180
Marginal R² / Conditional R²	0.127 / 0.160			0.279 / 0.799

The marginal R-squared considers only the variance of the fixed effects, while the conditional R-squared takes both the fixed and random effects into account.

The p-value is a simple approximation, based on the t-statistics and using the normal distribution function. A more precise p-value can be computed using p.val = "kr". In this case, which only applies to linear mixed models, the computation of p-values is based on conditional F-tests with Kenward-Roger approximation for the degrees of freedom (using the using the pbkrtest-package). Note that here the computation is more time consuming and thus not used as default. You can also display the approximated degrees of freedom with show.df.

tab_model(m1, p.val = "kr", show.df = TRUE)

	Negative impact with 7 items
Predictors	Estimates	CI	p	df
(Intercept)	6.55	4.82 – 8.28	<0.001	136.86
carer’ age	-0.00	-0.03 – 0.02	0.810	255.72
carer’s gender	0.47	-0.08 – 1.02	0.095	881.58
elder’s dependency	1.45	1.19 – 1.71	<0.001	883.58
Random Effects
σ²	12.61
τ₀₀_cluster	0.50
ICC	0.04
N _cluster	8
Observations	888
Marginal R² / Conditional R²	0.127 / 0.160

Generalized linear mixed models

tab_model() can also print and combine models with different link-functions.

data("efc")
efc$neg_c_7d <- ifelse(efc$neg_c_7 < median(efc$neg_c_7, na.rm = TRUE), 0, 1)
efc$cluster <- as.factor(efc$e15relat)
m3 <- glmer(
  neg_c_7d ~ c160age + c161sex + e42dep + (1 | cluster),
  data = efc, 
  family = binomial(link = "logit")
)

tab_model(m1, m3)

	Negative impact with 7 items			neg_c_7d
Predictors	Estimates	CI	p	Odds Ratios	CI	p
(Intercept)	6.55	4.86 – 8.23	<0.001	0.02	0.01 – 0.05	<0.001
carer’ age	-0.00	-0.03 – 0.02	0.802	1.01	0.99 – 1.02	0.355
carer’s gender	0.47	-0.08 – 1.02	0.094	1.83	1.30 – 2.59	0.001
elder’s dependency	1.45	1.19 – 1.71	<0.001	2.37	1.99 – 2.81	<0.001
Random Effects
σ²	12.61			3.29
τ₀₀	0.50 _cluster			0.24 _cluster
ICC	0.04			0.07
N	8 _cluster			8 _cluster
Observations	888			888
Marginal R² / Conditional R²	0.127 / 0.160			0.181 / 0.237

More complex models

Finally, an example from the glmmTMB-package to show how easy it is to print zero-inflated generalized linear mixed models as HTML table.

library(glmmTMB)
data("Salamanders")
m4 <- glmmTMB(
  count ~ spp + mined + (1 | site),
  ziformula = ~ spp + mined, 
  family = truncated_poisson(link = "log"), 
  data = Salamanders
)

tab_model(m1, m3, m4, show.ci = FALSE)

	Negative impact with 7 items		neg_c_7d		count
Predictors	Estimates	p	Odds Ratios	p	Incidence Rate Ratios	p
(Intercept)	6.55	<0.001	0.02	<0.001	0.94	0.745
carer’ age	-0.00	0.802	1.01	0.355
carer’s gender	0.47	0.094	1.83	0.001
elder’s dependency	1.45	<0.001	2.37	<0.001
spp: PR					0.59	0.062
spp: DM					1.25	0.121
spp: EC-A					0.82	0.331
spp: EC-L					1.91	<0.001
spp: DES-L					1.83	<0.001
spp: DF					1.05	0.765
mined: no					2.76	<0.001
Zero-Inflated Model
(Intercept)					5.79	<0.001
spp: PR					5.36	<0.001
spp: DM					0.65	0.223
spp: EC-A					3.02	0.003
spp: EC-L					0.65	0.223
spp: DES-L					0.51	0.056
spp: DF					0.65	0.223
mined: no					0.09	<0.001
Random Effects
σ²	12.61		3.29		0.29
τ₀₀	0.50 _cluster		0.24 _cluster		0.05 _site
ICC	0.04		0.07		0.15
N	8 _cluster		8 _cluster		23 _site
Observations	888		888		644
Marginal R² / Conditional R²	0.127 / 0.160		0.181 / 0.237		0.541 / 0.612

References

Nakagawa S, Johnson P, Schielzeth H (2017) The coefficient of determination R2 and intra-class correlation coefficient from generalized linear mixed-effects models revisted and expanded. J. R. Soc. Interface 14. doi: 10.1098/rsif.2017.0213

Daniel Lüdecke

2024-08-28

Mixed models summaries as HTML table

Generalized linear mixed models

More complex models

References