Performs hypothesis tests for arbitrary functions of the model parameters using the Delta method.
A list of fitted statistical models as produced by
A matrix or list containing the point estimates of the parameters for each imputed data set (see 'Details').
An array or list containing the variance-covariance matrix of the parameters for each imputed data set (see 'Details').
A character vector specifying constraints or functions of the vector of model parameters to be tested (see 'Details').
A character string denoting the method by which the test is performed. Can be
A character string denoting how the ARIV is calculated. Can be
(optional) A single number or a numeric vector denoting the complete-data degrees of freedom for the hypothesis test (see 'Details'). Only used if
This function performs tests of arbitrary functions (or constraints) of the model parameters using similar methods as
The function relies on the Delta method (e.g., Casella & Berger, 2002) for testing functions of the parameters and assumes that their sampling distribution is approximately normal.
The parameters can either be extracted automatically from the fitted statistical models (
model) or provided manually as matrices, arrays, or lists (
uhat, see 'Examples').
Constraints and other functions of the model parameters are specified in the
The constraints must be supplied as a character vector, where each string denotes a function or a constraint to be tested (see 'Examples').
The Wald-like tests that are carried out by
testConstraints are pooled across the imputed data sets with the D_1 (Li, Raghunathan & Rubin, 1991) or D_2 (Li, Meng, Raghunathan & Rubin, 1991) method, where D_1 operates on the constrained point and variance estimates, and D_2 operates on the Wald-statistics (for additional details, see
The pooled estimates and standard errors reported in the output are always based on D_1.
For D_1, the complete-data degrees of freedom can be adjusted for smaller samples by specifying
This function supports general statistical models that define
vcov methods (e.g.,
lavaan and others) as well as multilevel models estimated with
nlme and GEEs estimated with
uhat provide a general method for pooling parameter estimates regardless of model type (see 'Examples').
Support for further models may be added in future releases.
ariv argument determines how the average relative increase in variance (ARIV) is calculated (see
ariv = "default", the default estimators are used.
ariv = "positive", the default estimators are used but constrained to take on strictly positive values.
A list containing the results of the model comparison.
Casella, G., & Berger, R. L. (2002). Statistical inference (2nd. Ed.). Pacific Grove, CA: Duxbury.
Li, K.-H., Meng, X.-L., Raghunathan, T. E., & Rubin, D. B. (1991). Significance levels from repeated p-values with multiply-imputed data. Statistica Sinica, 1, 65-92.
Li, K. H., Raghunathan, T. E., & Rubin, D. B. (1991). Large-sample significance levels from multiply imputed data using moment-based statistics and an F reference distribution. Journal of the American Statistical Association, 86, 1065-1073.
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data(studentratings) fml <- MathDis + ReadDis + SchClimate ~ (1|ID) imp <- panImpute(studentratings, formula = fml, n.burn = 1000, n.iter = 100, m = 5) implist <- mitmlComplete(imp) # fit simple regression model fit.lm <- with(implist, lm(SchClimate ~ ReadDis + MathDis)) # apply Rubin's rules testEstimates(fit.lm) # * Example 1: test 'identity' function of two parameters (automatic) # test equivalent to model comparison with a restricted model (without 'ReadDis' # and 'MathDis') cons <- c("ReadDis", "MathDis") testConstraints(fit.lm, constraints = cons) # ... adjusting for finite samples testConstraints(fit.lm, constraints = cons, df.com = 749) # ... using D2 testConstraints(fit.lm, constraints = cons, method = "D2") # * Example 2: test for equality of two parameters # tests the hypothesis that the coefficients pertaining to 'ReadDis' and 'MathDis' # are equal (ReadDis = MathDis) cons <- c("ReadDis-MathDis") testConstraints(fit.lm, constraints = cons) # * Example 3: test against a fixed value # tests the hypothesis that the coefficient of "ReadDis" is equal to one # (i.e., 'ReadDis' - 1 == 0) cons <- c("ReadDis-1") testConstraints(fit.lm, constraints = cons) # * Example 4: test 'identity' function of two parameters (qhat, uhat) fit.lm <- with(implist, lm(SchClimate ~ ReadDis + MathDis)) qhat <- sapply(fit.lm, coef) uhat <- sapply(fit.lm, function(x) vcov(x), simplify = "array") cons <- c("ReadDis", "MathDis") testConstraints(qhat = qhat, uhat = uhat, constraints = cons)
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