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The D3-statistic is a likelihood-ratio test statistic.


D3(fit1, fit0 = NULL, dfcom = NULL, = NULL)



An object of class mira, produced by with().


An object of class mira, produced by with(). The model in fit0 is a nested within fit1. The default null model fit0 = NULL compares fit1 to the intercept-only model.


A single number denoting the complete-data degrees of freedom of model fit1. If not specified, it is set equal to df.residual of model fit1. If that cannot be done, the procedure assumes (perhaps incorrectly) a large sample.



An object of class mice.anova


The D3() function implement the LR-method by Meng and Rubin (1992). The implementation of the method relies on the broom package, the standard update mechanism for statistical models in R and the offset function.

The function calculates m repetitions of the full (or null) models, calculates the mean of the estimates of the (fixed) parameter coefficients \(\beta\). For each imputed imputed dataset, it calculates the likelihood for the model with the parameters constrained to \(\beta\).

The mitml::testModels() function offers similar functionality for a subset of statistical models. Results of mice::D3() and mitml::testModels() differ in multilevel models because the testModels() also constrains the variance components parameters. For more details on


Meng, X. L., and D. B. Rubin. 1992. Performing Likelihood Ratio Tests with Multiply-Imputed Data Sets. Biometrika, 79 (1): 103–11.

See also


# Compare two linear models:
imp <- mice(nhanes2, seed = 51009, print = FALSE)
mi1 <- with(data = imp, expr = lm(bmi ~ age + hyp + chl))
mi0 <- with(data = imp, expr = lm(bmi ~ age + hyp))
D3(mi1, mi0)
#>    test statistic df1      df2 dfcom  p.value      riv
#>  1 ~~ 2  2.917381   1 8.764849    20 0.122711 2.082143
if (FALSE) {
# Compare two logistic regression models
imp <- mice(boys, maxit = 2, print = FALSE)
fit1 <- with(imp, glm(gen > levels(gen)[1] ~ hgt + hc + reg, family = binomial))
fit0 <- with(imp, glm(gen > levels(gen)[1] ~ hgt + hc, family = binomial))
D3(fit1, fit0)