On structural equation modeling with data that are not missing completely at random

Abstract

A general latent variable model is given which includes the specification of a missing data mechanism. This framework allows for an elucidating discussion of existing general multivariate theory bearing on maximum likelihood estimation with missing data. Here, missing completely at random is not a prerequisite for unbiased estimation in large samples, as when using the traditional listwise or pairwise present data approaches. The theory is connected with old and new results in the area of selection and factorial invariance. It is pointed out that in many applications, maximum likelihood estimation with missing data may be carried out by existing structural equation modeling software, such as LISREL and LISCOMP. Several sets of artifical data are generated within the general model framework. The proposed estimator is compared to the two traditional ones and found superior.

Utilization of Mental Health Services by Minority Urban Adults: Psychosocial Predictors

“…The structural equation algorithm in Mplus dealt with missing data by using maximum likelihood estimation. 55 Table 2 presents the descriptive statistics, including the means and standard deviations (or percentages) of the dependent, independent, and control variables with comparisons by gender and ethnicity. Women were more educated than men in emerging adulthood and utilized more mental health services in the mid-30s.…”

A primer for the estimation of structural equation models in the presence of missing data: Maximum likelihood algorithms

“…This is problematic as the structural paths are typically the primary interest in structural equation modelling analyses. 46 Notice also that the level of bias was not trivial, and was either close to or exceeded the problematic criterion suggested by Muthén et al 47 In some cases, bias may be tolerable if an estimator yields highly efficient parameter estimates. The efficiency of the estimator may compensate for bias, resulting in parameter estimates that are, on average, closer to the true population value compared to an unbiased but inefficient estimator.…”

“…In addition, data in commercial marketing research studies are often not completely missing at random (ie MCAR) due to structural skip patterns generally reflecting respondents' unfamiliarity with a block of questions. Since the MCAR assumption may not hold in many applied situations, 49,50 most marketing researchers are facing MAR conditions and the choice of missing data technique becomes an important data analytic decision. Recall that under MAR, maximum likelihood estimators yield substantially less bias in parameter estimates than more traditional methods.…”

“…6 This method is referred to as the multiple-group approach, as its mathematical form is similar to the LISREL estimator used for multiple-group structural equation modelling analyses. This method has not experienced widespread use due to its programming complexity and the fact that it is practically restricted to situations that have a small number of distinct missing data patterns.…”

“…41 While judging the practical impact of bias is subjective, Muthén et al suggests that bias levels less than 10 per cent are probably not problematic. 42 Table 1 also gives the percentage of model rejections based on 2 goodness-of-fit tests (p Ͻ 0.05). While most of the percentages were relatively close to the nominal rate, pairwise deletion rejection rates approach 20 per cent.…”