### Journals Information

**
Mathematics and Statistics Vol. 11(1), pp. 134 - 143 DOI: 10.13189/ms.2023.110115 Reprint (PDF) (306Kb) **

## On the Performance of Full Information Maximum Likelihood in SEM Missing Data

**Amal HMIMOU ^{1}^{,*}, M'barek IAOUSSE ^{2}, Soumaia HMIMOU ^{3}, Hanaa HACHIMI ^{4}, Youssfi EL KETTANI ^{1}**

^{1}Laboratory of Partial Differential Equations, Spectral Algebra and Geometry, Department of Mathematics, Ibn Tofail University, Kenitra, Morocco

^{2}C3S Laboratory, Hassan II University of Casablanca, Morocco

^{3}Department of Biology, Ibn Tofail University, Kenitra, Morocco

^{4}Department of Mathematics, Sultan Moulay Slimane University, Beni Mellal, Morocco

**ABSTRACT**

Missing data is a real problem in all statistical modeling fields, particularly, in structural equation modeling which is a set of statistical techniques used to estimate models with latent concepts. In this research paper, an investigation of the techniques used to handle missing data in structural equation models is elaborated. To clarify this, a presentation of the mechanisms of missing data is made based on the probability distribution. This presentation recognizes three mechanisms: missing completely at random, missing at random, and missing not at random. Ignoring missing data in the statistical analysis may mislead the estimation and generates biased estimates. Many techniques are used to remedy this problem. In the present paper, we have presented three of them, namely, listwise deletion, pairwise deletion, and full information maximum likelihood. To investigate the power of each of these methods while using structural equation models a simulation study is launched. Furthermore, an examination of the correlation between the exogenous latent variables is done to extend the previous studies. We simulated a three latent variable structural model each with three observed variables. Three sample sizes (700, 1000, 1500) are examined accordingly to three missing rates for two specified mechanisms (2%, 10%, 15%). In addition, for each sample hundred other samples were generated and investigated using the same case design. The criteria of examination are a parameter bias calculated for each case design. The results illustrate as theoretically expected the following: (1) the non-convergence of pairwise deletion, (2) a huge loss of information when using listwise deletion, and (3) a relative performance for the full information maximum likelihood compared to listwise deletion when using the parameters bias as a criterion, particularly, for the correlation between the exogenous latent variables. This performance is revealed, chiefly, for larger sample sizes where the multivariate normal distribution occurs.

**KEYWORDS**

Structural Equation Modeling, MCAR, MAR, Missing Data, Parameter Bias

**Cite This Paper in IEEE or APA Citation Styles**

(a). IEEE Format:

[1] Amal HMIMOU , M'barek IAOUSSE , Soumaia HMIMOU , Hanaa HACHIMI , Youssfi EL KETTANI , "On the Performance of Full Information Maximum Likelihood in SEM Missing Data," Mathematics and Statistics, Vol. 11, No. 1, pp. 134 - 143, 2023. DOI: 10.13189/ms.2023.110115.

(b). APA Format:

Amal HMIMOU , M'barek IAOUSSE , Soumaia HMIMOU , Hanaa HACHIMI , Youssfi EL KETTANI (2023). On the Performance of Full Information Maximum Likelihood in SEM Missing Data. Mathematics and Statistics, 11(1), 134 - 143. DOI: 10.13189/ms.2023.110115.