Parametric bootstrap under model mis-specification

Lu, Hui; Young, George A.

doi:10.1016/j.csda.2012.01.018

Cited by 1 publication

(3 citation statements)

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“…In particular, the LM(H) and LM(S) tests have the worst performance in terms of power under small sample sizes. The bootstrap hypothesis testing does not depend on the asymptotic distribution of the test statistic under the null hypothesis and can be a good alternative under model misspecification (Lu and Young 2012).…”

Section: An Application To a Real Data Setmentioning

confidence: 99%

“…Responses of ''both'' for all items are coded as ''1'' and refer to ''egalitarian'' answers. For the same sample of women, in addition to the bootstrap hypothesis testing does not depend on the asymptotic distribution of the test statistic under the null hypothesis and can be a good alternative under model misspecification (Lu and Young, 2012). The first step of the bootstrap hypothesis testing procedure is to generate B bootstrap samples, or simulated data sets, indexed by h, that should satisfy the null hypothesis (Efron and Tibshirani, 1994).…”

Section: An Application To a Real Data Setmentioning

confidence: 99%

“…For this reason, the values of the group variable in each bootstrap sample are randomly drawn from a Bernoulli variable with success probability estimated on the original sample of observations. The parametric bootstrap can be used even when the model under the null hypothesis is misspecified (Lu and Young, 2012). The bootstrap hypothesis testing is composed using the following steps (Efron and Tibshirani, 1994) When t is pivotal, that is its distribution does not depend on unknown parameters, and the number of bootstrap samples B is such that a(B + 1) is an integer, the bootstrap hypothesis testing procedure can yield exact test (Dwass, 1957).…”

Section: An Application To a Real Data Setmentioning

confidence: 99%

See 2 more Smart Citations

Use of the Lagrange Multiplier Test for Assessing Measurement Invariance Under Model Misspecification

Guastadisegni

Cagnone

Moustaki

et al. 2021

Educational and Psychological Measurement

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This article studies the Type I error, false positive rates, and power of four versions of the Lagrange multiplier test to detect measurement noninvariance in item response theory (IRT) models for binary data under model misspecification. The tests considered are the Lagrange multiplier test computed with the Hessian and cross-product approach, the generalized Lagrange multiplier test and the generalized jackknife score test. The two model misspecifications are those of local dependence among items and nonnormal distribution of the latent variable. The power of the tests is computed in two ways, empirically through Monte Carlo simulation methods and asymptotically, using the asymptotic distribution of each test under the alternative hypothesis. The performance of these tests is evaluated by means of a simulation study. The results highlight that, under mild model misspecification, all tests have good performance while, under strong model misspecification, the tests performance deteriorates, especially for false positive rates under local dependence and power for small sample size under misspecification of the latent variable distribution. In general, the Lagrange multiplier test computed with the Hessian approach and the generalized Lagrange multiplier test have better performance in terms of false positive rates while the Lagrange multiplier test computed with the cross-product approach has the highest power for small sample sizes. The asymptotic power turns out to be a good alternative to the classic empirical power because it is less time consuming. The Lagrange tests studied here have been also applied to a real data set.

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Section: An Application To a Real Data Setmentioning

confidence: 99%

Section: An Application To a Real Data Setmentioning

confidence: 99%