### Abstract

This paper presents a comparison of results from two methods for estimating and testing a model for the factor analysis of dichotomous variables. For k manifest dichotomous variables, the data can be cross‐classified to form a vector of 2^{k} frequencies, and nonlinear methods that use the full information in these 2^{k} frequencies are available for factor analysis. In addition, another method that uses only the limited information in the first‐, and second‐order marginal frequencies is available for the same model. As k becomes larger, substantial differences between the full‐information and limited‐information methods become apparent in results from the test of fit. For large k. Type I and Type II error rates may be higher in the full‐information approach, because as the vector of 2^{k} frequencies becomes sparse, the chi‐square approximation for the distribution of the goodness‐of‐fit test statistic becomes poorer. In this paper, Monte Carlo experiments are used under a variety of conditions to compare the methods for rate of Type I errors when the model matches the simulated data and for the rate of Type II errors when the model does not match the simulated data. 1994 The British Psychological Society

Original language | English (US) |
---|---|

Pages (from-to) | 85-107 |

Number of pages | 23 |

Journal | British Journal of Mathematical and Statistical Psychology |

Volume | 47 |

Issue number | 1 |

DOIs | |

State | Published - 1994 |

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### ASJC Scopus subject areas

- Statistics and Probability
- Arts and Humanities (miscellaneous)
- Psychology(all)

### Cite this

**Validity of the chi‐square test in dichotomous variable factor analysis when expected frequencies are small.** / Reiser, Mark; VandenBerg, Maria.

Research output: Contribution to journal › Article

*British Journal of Mathematical and Statistical Psychology*, vol. 47, no. 1, pp. 85-107. https://doi.org/10.1111/j.2044-8317.1994.tb01026.x

}

TY - JOUR

T1 - Validity of the chi‐square test in dichotomous variable factor analysis when expected frequencies are small

AU - Reiser, Mark

AU - VandenBerg, Maria

PY - 1994

Y1 - 1994

N2 - This paper presents a comparison of results from two methods for estimating and testing a model for the factor analysis of dichotomous variables. For k manifest dichotomous variables, the data can be cross‐classified to form a vector of 2k frequencies, and nonlinear methods that use the full information in these 2k frequencies are available for factor analysis. In addition, another method that uses only the limited information in the first‐, and second‐order marginal frequencies is available for the same model. As k becomes larger, substantial differences between the full‐information and limited‐information methods become apparent in results from the test of fit. For large k. Type I and Type II error rates may be higher in the full‐information approach, because as the vector of 2k frequencies becomes sparse, the chi‐square approximation for the distribution of the goodness‐of‐fit test statistic becomes poorer. In this paper, Monte Carlo experiments are used under a variety of conditions to compare the methods for rate of Type I errors when the model matches the simulated data and for the rate of Type II errors when the model does not match the simulated data. 1994 The British Psychological Society

AB - This paper presents a comparison of results from two methods for estimating and testing a model for the factor analysis of dichotomous variables. For k manifest dichotomous variables, the data can be cross‐classified to form a vector of 2k frequencies, and nonlinear methods that use the full information in these 2k frequencies are available for factor analysis. In addition, another method that uses only the limited information in the first‐, and second‐order marginal frequencies is available for the same model. As k becomes larger, substantial differences between the full‐information and limited‐information methods become apparent in results from the test of fit. For large k. Type I and Type II error rates may be higher in the full‐information approach, because as the vector of 2k frequencies becomes sparse, the chi‐square approximation for the distribution of the goodness‐of‐fit test statistic becomes poorer. In this paper, Monte Carlo experiments are used under a variety of conditions to compare the methods for rate of Type I errors when the model matches the simulated data and for the rate of Type II errors when the model does not match the simulated data. 1994 The British Psychological Society

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U2 - 10.1111/j.2044-8317.1994.tb01026.x

DO - 10.1111/j.2044-8317.1994.tb01026.x

M3 - Article

AN - SCOPUS:85004830124

VL - 47

SP - 85

EP - 107

JO - British Journal of Mathematical and Statistical Psychology

JF - British Journal of Mathematical and Statistical Psychology

SN - 0007-1102

IS - 1

ER -