Analysis of Interactions and Nonlinear Effects with Missing Data: A Factored Regression Modeling Approach Using Maximum Likelihood Estimation

An Investigation of Factored Regression Missing Data Methods for Multilevel Models with Cross-Level Interactions

A growing body of literature has focused on missing data methods that factorize the joint distribution into a part representing the analysis model of interest and a part representing the distributions of the incomplete predictors. Relatively little is known about the utility of this method for multilevel models with interactive effects. This study presents a series of Monte Carlo computer simulations that investigates Bayesian and multiple imputation strategies based on factored regressions. When the model's distributional assumptions are satisfied, these methods generally produce nearly unbiased estimates and good coverage, with few exceptions. Severe misspecifications that arise from substantially non-normal distributions can introduce biased estimates and poor coverage. Follow-up simulations suggest that a Yeo-Johnson transformation can mitigate these biases. A real data example illustrates the methodology, and the paper suggests several avenues for future research.

Response Surface Analysis with Missing Data

Response Surface Analysis (RSA) is gaining popularity in psychological research as a tool for investigating congruence hypotheses (e.g., consequences of self-other agreement, person-job fit, dyadic similarity). RSA involves the estimation of a nonlinear polynomial regression model and the interpretation of the resulting response surface. However, little is known about how best to conduct RSA when the underlying data are incomplete. In this article, we compare different methods for handling missing data in RSA. This includes different strategies for multiple imputation (MI) and maximum-likelihood (ML) estimation. Specifically, we consider the "just another variable" (JAV) approach to MI and ML, an approach that is in regular use in applications of RSA, and the more novel "substantive-model-compatible" (SMC) approach. In a simulation study, we evaluate the impact of these methods on focal outcomes of RSA, including the accuracy of parameter estimates, the shape of the response surface, and the testing of congruence hypotheses. Our findings suggest that the JAV approach can sometimes distort parameter estimates and conclusions about the shape of the response surface, whereas the SMC approach performs well overall. We illustrate applications of the methods in a worked example with real data and provide recommendations for their application in practice.

The brief sense of community scale: Testing dimensionality and measurement invariance by gender among Hispanic/Latinx youth

Psychological sense of community is defined as feelings of belongingness and a shared belief that community members will meet one another's needs. Psychological sense of community has four dimensions: membership, influence, needs fulfillment, and emotional connection. In this study, multigroup confirmatory factor analysis was used to examine the first and second-order factor structure of the brief sense of community scale (BSCS) between male and female Hispanic/Latinx adolescents from an urban community (N = 947). To help validate the BSCS model, the second-order factor model was tested with regression to predict the measures of intrapersonal psychological empowerment and ethnic identity, as constructs conceptually related to psychological sense of community. Findings support that: (1) psychological sense of community can be measured through the BSCS and as a four-factor model among Hispanic/Latinx youth, supporting McMillan and Chavis's (1986) original theoretical discussions; (2) while no differences between genders were present at the model-level, there was path-specific variation; and (3) intrapersonal psychological empowerment and ethnic identity were associated with psychological sense of community.

An Introduction to Factored Regression Models with Blimp

In this paper, we provide an introduction to the factored regression framework. This modeling framework applies the rules of probability to break up or “factor” a complex joint distribution into a product of conditional regression models. Using this framework, we can easily specify the complex multivariate models that missing data modeling requires. The article provides a brief conceptual overview of factored regression and describes the functional notation used to conceptualize the models. Furthermore, we present a conceptual overview of how the models are estimated and imputations are obtained. Finally, we discuss how users can use the free software package, Blimp, to estimate the models in the context of a mediation example.

The establishment and evaluation of a new model for the prediction of Children B-ALL based on TARGET: A SQUIRE-compliant study

B lymphocytic leukemia (B-ALL) is a hematopoietic malignant disease characterized by an accumulation of early B cells. This study aimed to construct a children B-ALL Nomogram prediction model based on Therapeutically Applicable Research to Generate Effective Treatments database, so as to further guide clinical diagnose and treatment.Clinical data related to children B-ALL were collected from the TARGET database, among which, the stage II clinical data were used as the prediction model, while the stage I clinical data were utilized as the external verification model. The stage II clinical factors were analyzed through Lasso regression analysis to screen the risk factors for the construction of Nomogram prediction model. In addition, the model prediction capacity and accuracy were verified internally and externally using the ROC curve, C-index and calibration curve, respectively.A total of 1316 B-ALL children were enrolled in this study. Lasso regression analysis revealed that, Age, Gender, WBC, CNSL, MRD29, BMR, CNS R, BCR-ABL1, BMA29, DS, and DI were the important prognostic risk factors. The C-index values of internal and external verification models were 0.870 and 0.827, respectively, revealing the ideal model discriminating capacity. Besides, the calibration curve had high contact ratio, which suggested favorable consistency between the incidence predicted by the model and the actual incidence. Moreover, the AUC values of the ROC curve were 0.858, 0.787, 0.898, and 0.867, respectively, indicating high model prediction accuracy in predicting the 3- and 5-year survival rates of children with B-ALL.The Nomogram prediction model plotted in this study exhibits favorable prediction capacity and clinical practicability for the survival rate of B-ALL children, which contributes to patients screening and clinical intervention.

Adherence to a plant-based, high-fibre dietary pattern is related to regression of non-alcoholic fatty liver disease in an elderly population

Dietary lifestyle intervention is key in treating non-alcoholic fatty liver disease (NAFLD). We aimed to examine the longitudinal relation between well-established dietary patterns as well as population-specific dietary patterns and NAFLD. Participants from two subsequent visits of the Rotterdam Study were included. All underwent serial abdominal ultrasonography (median follow-up: 4.4 years) and filled in a food frequency questionnaire. Secondary causes of steatosis were excluded. Dietary data from 389 items were collapsed into 28 food groups and a posteriori dietary patterns were identified using factor analysis. Additionally, we scored three a priori dietary patterns (Mediterranean Diet Score, Dutch Dietary Guidelines and WHO-score). Logistic mixed regression models were used to examine the relation between dietary patterns and NAFLD. Analyses were adjusted for demographic, lifestyle and metabolic factors. We included 963 participants of whom 343 had NAFLD. Follow-up data was available in 737 participants. Incident NAFLD was 5% and regressed NAFLD was 30%. We identified five a posteriori dietary patterns (cumulative explained variation [R²] = 20%). The patterns were characterised as: vegetable and fish, red meat and alcohol, traditional, salty snacks and sauces, high fat dairy & refined grains pattern. Adherence to the traditional pattern (i.e. high intake of vegetable oils/stanols, margarines/butters, potatoes, whole grains and sweets/desserts) was associated with regression of NAFLD per SD increase in Z-score (0.40, 95% CI 0.15–1.00). Adherence to the three a priori patterns all showed regression of NAFLD, but only the WHO-score showed a distinct association (0.73, 95% CI 0.53–1.00). Hence, in this large elderly population, adherence to a plant-based, high-fibre and low-fat diet was related to regression of NAFLD.