### Abstract

This paper discusses power and sample-size computation for likelihood ratio and Wald testing of the significance of covariate effects in latent class models. For both tests, asymptotic distributions can be used; that is, the test statistic can be assumed to follow a central Chi-square under the null hypothesis and a non-central Chi-square under the alternative hypothesis. Power or sample-size computation using these asymptotic distributions requires specification of the non-centrality parameter, which in practice is rarely known. We show how to calculate this non-centrality parameter using a large simulated data set from the model under the alternative hypothesis. A simulation study is conducted evaluating the adequacy of the proposed power analysis methods, determining the key study design factor affecting the power level, and comparing the performance of the likelihood ratio and Wald test. The proposed power analysis methods turn out to perform very well for a broad range of conditions. Moreover, apart from effect size and sample size, an important factor affecting the power is the class separation, implying that when class separation is low, rather large sample sizes are needed to achieve a reasonable power level.

Original language | English |
---|---|

Pages (from-to) | 1824-1837 |

Journal | Behavior Research Methods |

Volume | 49 |

Issue number | 5 |

DOIs | |

Publication status | Published - Oct 2017 |

### Keywords

- Latent class
- Power analysis
- Likelihood ratio
- Wald test
- Asymptotic distributions
- Non-centrality parameter
- Large simulated data set
- SAMPLE-SIZE
- LOGISTIC-REGRESSION
- NUMBER

### Cite this

*Behavior Research Methods*,

*49*(5), 1824-1837. https://doi.org/10.3758/s13428-016-0825-y

}

*Behavior Research Methods*, vol. 49, no. 5, pp. 1824-1837. https://doi.org/10.3758/s13428-016-0825-y

**Statistical power of likelihood ratio and Wald tests in latent class models with covariates.** / Gudicha, D.W.; Schmittmann, V.D.; Vermunt, J.K.

Research output: Contribution to journal › Article › Scientific › peer-review

TY - JOUR

T1 - Statistical power of likelihood ratio and Wald tests in latent class models with covariates

AU - Gudicha, D.W.

AU - Schmittmann, V.D.

AU - Vermunt, J.K.

PY - 2017/10

Y1 - 2017/10

N2 - This paper discusses power and sample-size computation for likelihood ratio and Wald testing of the significance of covariate effects in latent class models. For both tests, asymptotic distributions can be used; that is, the test statistic can be assumed to follow a central Chi-square under the null hypothesis and a non-central Chi-square under the alternative hypothesis. Power or sample-size computation using these asymptotic distributions requires specification of the non-centrality parameter, which in practice is rarely known. We show how to calculate this non-centrality parameter using a large simulated data set from the model under the alternative hypothesis. A simulation study is conducted evaluating the adequacy of the proposed power analysis methods, determining the key study design factor affecting the power level, and comparing the performance of the likelihood ratio and Wald test. The proposed power analysis methods turn out to perform very well for a broad range of conditions. Moreover, apart from effect size and sample size, an important factor affecting the power is the class separation, implying that when class separation is low, rather large sample sizes are needed to achieve a reasonable power level.

AB - This paper discusses power and sample-size computation for likelihood ratio and Wald testing of the significance of covariate effects in latent class models. For both tests, asymptotic distributions can be used; that is, the test statistic can be assumed to follow a central Chi-square under the null hypothesis and a non-central Chi-square under the alternative hypothesis. Power or sample-size computation using these asymptotic distributions requires specification of the non-centrality parameter, which in practice is rarely known. We show how to calculate this non-centrality parameter using a large simulated data set from the model under the alternative hypothesis. A simulation study is conducted evaluating the adequacy of the proposed power analysis methods, determining the key study design factor affecting the power level, and comparing the performance of the likelihood ratio and Wald test. The proposed power analysis methods turn out to perform very well for a broad range of conditions. Moreover, apart from effect size and sample size, an important factor affecting the power is the class separation, implying that when class separation is low, rather large sample sizes are needed to achieve a reasonable power level.

KW - Latent class

KW - Power analysis

KW - Likelihood ratio

KW - Wald test

KW - Asymptotic distributions

KW - Non-centrality parameter

KW - Large simulated data set

KW - SAMPLE-SIZE

KW - LOGISTIC-REGRESSION

KW - NUMBER

U2 - 10.3758/s13428-016-0825-y

DO - 10.3758/s13428-016-0825-y

M3 - Article

VL - 49

SP - 1824

EP - 1837

JO - Behavior Research Methods

JF - Behavior Research Methods

SN - 1554-351X

IS - 5

ER -