Open Access

Despite the well-documented link between child maltreatment (CM) and mental health, evidence suggests substantial variability in the post-traumatic sequelae of CM across cultures. The perceived acceptability of CM in one’s community might moderate the association between CM and mental health, but little research has been conducted on it so far. This study examined how the perceived acceptability of CM may influence the relationship between CM experiences and post-traumatic symptoms in individuals from four different continents and if the pattern of associations is the same across countries. We recruited a sample of 478 adults from Cameroon (n = 111), Canada (n = 137), Japan (n = 108), and Germany (n = 122). We administered online questionnaires and performed multiple group moderation analyses for total CM, neglect, physical abuse, emotional maltreatment, sexual abuse, and exposure to domestic violence (DV). A significant positive main effect of CM on post-traumatic symptoms was found in the overall sample and in Cameroon; in Germany, only neglect and emotional maltreatment were positively associated to post-traumatic symptoms. Moderation effects were identified; the perceived acceptability of neglect in Cameroon and Germany and of exposure to DV in Cameroon had a dampening effect on the relationship between CM experiences and post-traumatic symptoms. Our findings confirm that CM experiences entail long-term post-traumatic sequelae that can vary across cultures and CM subtypes and further our understanding of this issue by showing that the perceived acceptability of CM may be an understudied moderator.

The present study investigates the role of sense of belonging on dropout intention in teacher education with a special focus on immigrant teacher students. We present data from a survey of 925 German teacher students using two times of measurement. The results confirm the significance of sense of belonging for the dropout rate among students in teacher education and support our hypotheses that immigrant students show a lower sense of belonging and higher dropout intentions.

We provide a framework for motivating and diagnosing the functional form in the structural part of nonlinear or linear structural equation models when the measurement model is a correctly specified linear confirmatory factor model. A mathematical population-based analysis provides asymptotic identification results for conditional expectations of a coordinate of an endogenous latent variable given exogenous and possibly other endogenous latent variables, and theoretically well-founded estimates of this conditional expectation are suggested. Simulation studies show that these estimators behave well compared to presently available alternatives. Practically, we recommend the estimator using Bartlett factor scores as input to classical non-parametric regression methods.

Closed-form (asymptotic) analytical power estimation is only available for limited classes of models, requiring correct model specification for most applications. Simulation-based power estimation can be applied in almost all scenarios where data following the model can be estimated. However, a general framework for calculating the required sample sizes for given power rates is still lacking. We propose a new model-implied simulation-based power estimation (MSPE) method for the z-test that makes use of the asymptotic normality property of estimates of a wide class of estimators, the M-estimators, and give theoretical justification for the approach. M-estimators include maximum-likelihood, least squares estimates and limited information estimators, but also estimators used for misspecified models, hence, the new simulation-based power modeling method is widely applicable. The MSPE employs a parametric model to describe the relationship between power and sample size, which can then be used to determine the required sample size for a specified power rate. We highlight its performance in linear and nonlinear structural equation models (SEM) for correctly specified models and models under distributional misspecification. Simulation results suggest that the new power modeling method is unbiased and shows good performance with regard to root mean squared error and type I error rates for the predicted required sample sizes and predicted power rates, outperforming alternative approaches, such as the naïve approach of selecting a discrete selection of sample sizes with linear interpolation of power or simple logistic regression approaches. The MSPE appears to be a valuable tool to estimate power for models without an (asymptotic) analytical power estimation.

In the social sciences, relations among latent variables are of great interest. These associations are not necessarily linear, and selecting the correct model is of significant importance; otherwise, the inferences drawn from these models might be arbitrarily wrong. Latent variables cannot be measured directly but are operationalized indirectly via multiple indicators. Structural Equation Modeling (SEM) is used to examine the associations between latent variables through the correlational structure in multiple measurements (Bollen, 1989). The model selection process is guided by (robust) model fit tests, such as the (robust) χ2-test (e.g., Satorra & Bentler, 2010) in linear SEM analysis. Although there are extensions for specific quadratic and interaction SEM (QISEM, Büchner & Klein, 2020), these model fit tests are not generally applicable to nonlinear SEM (NLSEM) due to the lack of a saturated comparison model (Büchner & Klein, 2020; Mooijaart & Satorra, 2009). In regression analysis, non-parametric trend estimates and scatterplots can be used to examine the structural form and guide model selection. However, these are not suitable for NLSEM due to measurement errors in the observations. Latent variables cannot be observed directly, but estimates for these are available by using factor scores. Factor scores are transformations of the data that estimate the latent variables with approximation error. Still, factor scores are indeterminate (Grice, 2001), meaning that several approaches will result in different results. However, as the number of measurements increases, the approximation error diminishes, and factor scores become close estimates of the latent variables. In this thesis in Manuscript A, a simple set of assumptions is derived to identify the trends in NLSEM using linear factor scores. These trends are described by the conditional expectation of endogenous variables given exogenous variables. Identification means that the trends can be estimated from observed data. Linear factor scores are simple linear transformations of the data and therefore are straightforward to compute. However, due to the approximation error in linear factor scores, these assumptions are asymptotic in nature, as they are only applicable for a large number of measurements per latent variable, as then the prediction error becomes negligible or can be explicitly modeled. In contrast to previous identification results (Kelava et al., 2017), these asymptotic assumptions used in this thesis allow for cross-relations between the measurements within the exogenous part of the model and within the endogenous part of the model. This implies that cross-loadings and residual covariances are permitted within measurements of the exogenous latent variables (ξ) and within measurements of the endogenous latent variables (η), while cross-relations between measurements of the exogenous part and the endogenous part of the model are disallowed. Independence assumptions on the measurement errors of the exogenous and endogenous parts of the model, along with independence from the latent variables, imply that the Bartlett (1937) factor score (BFS) has a specific structure that connects it to the literature on non-parametric regression with measurement error (Delaigle et al., 2009; Huang & Zhou, 2017). Although, in this literature, the distribution of the measurement error is assumed to be known, this similarity, combined with continuity assumptions on the nonlinear trend, can be used to identify the conditional expectation. This is shown mathematically in Manuscript A. Consequently, trends in NLSEM can be estimated using BFS under the given assumptions either by ignoring the approximation error or by explicitly modeling the approximation error. For a large number of measurements in the exogenous part of the model, the approximation error variance of the BFS on the exogenous part of the model is small. Therefore, this approximation error can be ignored by inputting BFS into non-parametric regression methods such as the LOESS (locally estimated scatterplot smoothing, Cleveland, 1979, 1981). Since BFS are linear transformations of the data, a central limits effect occurs on the approximation error.