Generalized Linear Factor Score Regression: A Comparison of Four Methods.

Factor score regression has recently received growing interest as an alternative for structural equation modeling. However, many applications are left without guidance because of the focus on normally distributed outcomes in the literature. We perform a simulation study to examine how a selection of factor scoring methods compare when estimating regression coefficients in generalized linear factor score regression. The current study evaluates the regression method and the correlation-preserving method as well as two sum score methods in ordinary, logistic, and Poisson factor score regression. Our results show that scoring method performance can differ notably across the considered regression models. In addition, the results indicate that the choice of scoring method can substantially influence research conclusions. The regression method generally performs the best in terms of coefficient and standard error bias, accuracy, and empirical Type I error rates. Moreover, the regression method and the correlation-preserving method mostly outperform the sum score methods.

A unified model-implied instrumental variable approach for structural equation modeling with mixed variables.

The model-implied instrumental variable (MIIV) estimator is an equation-by-equation estimator of structural equation models that is more robust to structural misspecifications than full information estimators. Previous studies have concentrated on endogenous variables that are all continuous (MIIV-2SLS) or all ordinal . We develop a unified MIIV approach that applies to a mixture of binary, ordinal, censored, or continuous endogenous observed variables. We include estimates of factor loadings, regression coefficients, variances, and covariances along with their asymptotic standard errors. In addition, we create new goodness of fit tests of the model and overidentification tests of single equations. Our simulation study shows that the proposed MIIV approach is more robust to structural misspecifications than diagonally weighted least squares (DWLS) and that both the goodness of fit model tests and the overidentification equations tests can detect structural misspecifications. We also find that the bias in asymptotic standard errors for the MIIV estimators of factor loadings and regression coefficients are often lower than the DWLS ones, though the differences are small in large samples. Our analysis shows that scaling indicators with low reliability can adversely affect the MIIV estimators. Also, using a small subset of MIIVs reduces small sample bias of coefficient estimates, but can lower the power of overidentification tests of equations.

Specification issues in nonlinear sem: the moderation that wasn't / Problemas de especificación en SEM no lineal: la moderación que no lo era

BACKGROUND: Analysis of interaction or moderation effects between latent variables is a common requirement in the social sciences. However, when predictors are correlated, interaction and quadratic effects become more alike, making them difficult to distinguish. As a result, when data are drawn from a quadratic population model and the analysis model specifies interactions only, misleading results may be obtained. METHOD: This article addresses the consequences of different types of specification error in nonlinear structural equation models using a Monte Carlo study. RESULTS: Results show that fitting a model with interactions when quadratic effects are present in the population will almost certainly lead to erroneous detection of moderation effects, and that the same is true in the opposite scenario. Simultaneous estimation of interactions and quadratic effects yields correct results. CONCLUSIONS: Simultaneous estimation of interaction and quadratic effects prevents detection of spurious or misleading nonlinear effects. Results are discussed and recommendations are offered to applied researchers

ANTECEDENTES: el análisis de efectos de interacción o moderación entre variables latentes es común en ciencias sociales. Sin embargo, cuando los predictores están correlacionados, los efectos de interacción y cuadráticos se vuelven parecidos, haciendo difícil su distinción. Así, cuando los datos provienen de un modelo de cuadrático a nivel poblacional y el modelo de análisis solo especifica interacciones, se pueden obtener resultados engañosos. MÉTODO: este artículo aborda las consecuencias de diferentes tipos de errores de especificación en modelos de ecuaciones estructurales no lineales utilizando un estudio de Monte Carlo. RESULTADOS: los resultados muestran que estimar un modelo con interacciones cuando en la población hay efectos cuadráticos conducirá a una detección equivocada de efectos de moderación con casi plena seguridad, y lo mismo ocurrirá en el escenario opuesto. La estimación simultánea de interacciones y efectos cuadráticos en el modelo conduce a resultados correctos. CONCLUSIONES: la estimación simultánea de efectos de interacción y cuadráticos permite evitar detectar efectos no lineales espurios o engañosos. Los resultados se discuten para ofrecer recomendaciones a los investigadores aplicados

Specification issues in nonlinear SEM: The moderation that wasn't.

BACKGROUND: Analysis of interaction or moderation effects between latent variables is a common requirement in the social sciences. However, when predictors are correlated, interaction and quadratic effects become more alike, making them difficult to distinguish. As a result, when data are drawn from a quadratic population model and the analysis model specifies interactions only, misleading results may be obtained. METHOD: This article addresses the consequences of different types of specification error in nonlinear structural equation models using a Monte Carlo study. RESULTS: Results show that fitting a model with interactions when quadratic effects are present in the population will almost certainly lead to erroneous detection of moderation effects, and that the same is true in the opposite scenario. Simultaneous estimation of interactions and quadratic effects yields correct results. CONCLUSIONS: Simultaneous estimation of interaction and quadratic effects prevents detection of spurious or misleading nonlinear effects. Results are discussed and recommendations are offered to applied researchers.

Approximated Penalized Maximum Likelihood for Exploratory Factor Analysis: An Orthogonal Case.

The problem of penalized maximum likelihood (PML) for an exploratory factor analysis (EFA) model is studied in this paper. An EFA model is typically estimated using maximum likelihood and then the estimated loading matrix is rotated to obtain a sparse representation. Penalized maximum likelihood simultaneously fits the EFA model and produces a sparse loading matrix. To overcome some of the computational drawbacks of PML, an approximation to PML is proposed in this paper. It is further applied to an empirical dataset for illustration. A simulation study shows that the approximation naturally produces a sparse loading matrix and more accurately estimates the factor loadings and the covariance matrix, in the sense of having a lower mean squared error than factor rotations, under various conditions.

Asymptotic Robustness Study of the Polychoric Correlation Estimation.

Asymptotic robustness against misspecification of the underlying distribution for the polychoric correlation estimation is studied. The asymptotic normality of the pseudo-maximum likelihood estimator is derived using the two-step estimation procedure. The t distribution assumption and the skew-normal distribution assumption are used as alternatives to the normal distribution assumption in a numerical study. The numerical results show that the underlying normal distribution can be substantially biased, even though skewness and kurtosis are not large. The skew-normal assumption generally produces a lower bias than the normal assumption. Thus, it is worth using a non-normal distributional assumption if the normal assumption is dubious.

Asymptotic efficiency of the pseudo-maximum likelihood estimator in multi-group factor models with pooled data.

A multi-group factor model is suitable for data originating from different strata. However, it often requires a relatively large sample size to avoid numerical issues such as non-convergence and non-positive definite covariance matrices. An alternative is to pool data from different groups in which a single-group factor model is fitted to the pooled data using maximum likelihood. In this paper, properties of pseudo-maximum likelihood (PML) estimators for pooled data are studied. The pooled data are assumed to be normally distributed from a single group. The resulting asymptotic efficiency of the PML estimators of factor loadings is compared with that of the multi-group maximum likelihood estimators. The effect of pooling is investigated through a two-group factor model. The variances of factor loadings for the pooled data are underestimated under the normal theory when error variances in the smaller group are larger. Underestimation is due to dependence between the pooled factors and pooled error terms. Small-sample properties of the PML estimators are also investigated using a Monte Carlo study.

ADHD symptoms, academic achievement, self-perception of academic competence and future orientation: a longitudinal study.

In the investigation of the effect of attention deficit hyperactivity disorder (ADHD) symptoms on school careers there is a need to study the role of adolescent and childhood ADHD symptoms and academic achievement, and to incorporate measures that include the individual's perspective. Our aim was to gain an overview of the long-term development of school careers in relation to ADHD symptoms. We studied associations between ADHD symptoms and academic achievement at different time-points and future orientation at the end of high school, and assessed the role of self-perceptions of academic competence in these associations. Participants were 192 children (47% girls) with a range of ADHD symptoms taken from a community sample. Collecting data at three time points, in 6th, 11th and 12th grade we tested a structural equation model. Results showed that ADHD symptoms in 6th grade negatively affected academic achievement concurrently and longitudinally. ADHD symptoms in 11th grade negatively affected concurrent academic achievement and academic self-perception and future orientation in 12th grade. Academic achievement had a positive influence on academic self-perception and future orientation. Given the other factors, self-perception of academic competence did not contribute to outcomes. We concluded that early ADHD symptoms may cast long shadows on young people's academic progress. This happens mainly by way of stability in symptoms and relations to early low academic achievement.

ML versus MI for Missing Data with Violation of Distribution Conditions.

Normal-distribution-based maximum likelihood (ML) and multiple imputation (MI) are the two major procedures for missing data analysis. This article compares the two procedures with respects to bias and efficiency of parameter estimates. It also compares formula-based standard errors (SEs) for each procedure against the corresponding empirical SEs. The results indicate that parameter estimates by MI tend to be less efficient than those by ML; and the estimates of variance-covariance parameters by MI are also more biased. In particular, when the population for the observed variables possesses heavy tails, estimates of variance-covariance parameters by MI may contain severe bias even at relative large sample sizes. Although performing a lot better, ML parameter estimates may also contain substantial bias at smaller sample sizes. The results also indicate that, when the underlying population is close to normally distributed, SEs based on the sandwich-type covariance matrix and those based on the observed information matrix are very comparable to empirical SEs with either ML or MI. When the underlying distribution has heavier tails, SEs based on the sandwich-type covariance matrix for ML estimates are more reliable than those based on the observed information matrix. Both empirical results and analysis show that neither SEs based on the observed information matrix nor those based on the sandwich-type covariance matrix can provide consistent SEs in MI. Thus, ML is preferable to MI in practice, although parameter estimates by MI might still be consistent.

The impact of folate status and folic acid supplementation on the micronucleus frequency in human erythrocytes.

Folic acid has a well-documented stabilising effect on chromosomes. A correlation between folate status and chromosome stability in humans has been reported in studies that were restricted to certain subpopulations, e.g., folate-deficient persons. The goal of the present investigation was to clarify if there also is a correlation between folate status and chromosome stability among individuals without any folate deficiency. The method used here is the recently developed flow cytometry-based micronucleus assay in human transferrin-positive reticulocytes (MN-Trf-Ret). In a blood sample, separation of the very young reticulocytes from the mature erythrocytes makes this micronucleus assay possible. This investigation comprises three studies (cross-sectional, giving baseline data), two of which are connected to an intervention study. In the three cross-sectional studies (total number of subjects, 99) the frequency of MN-Trf-Ret (fMN-Trf-Ret) was measured and compared with the serum folate status. In two of the studies also serum homocysteine and Vitamin B12 were measured and compared with the baseline fMN-Trf-Ret. Combining the results from the three cross-sectional studies, a negative correlation between folate status and fMN-Trf-Ret was obtained (p<0.05). The goal of the intervention studies was to clarify if different nutritional supplementations had any effect on the fMN-Trf-Ret and the cell proliferation (percentage polychromatic erythrocytes, PCE). Each of the two studies involved two groups, one placebo and one supplemented group. In one of the studies the supplementation was folic acid, 1000 microg/day during 1 week (n=30, both sexes); in the other intervention study, folic acid (800 microg/day), B12 (20 microg/day) and B6 (4 mg/day) were taken during 1 week (n=29, both sexes). No significant difference in %PCE or fMN-Trf-Ret between the two groups was found in either of the two intervention studies.