Practical problems that are frequently encountered in applications of covariance structure analysis are discussed and solutions are suggested. Conceptual, statistical, and practical requirements fo...

Practical Issues in Structural Modeling

Structural equation modeling (SEM) is a multivariate statistical framework that is used to model complex relationships between directly observed and indirectly observed (latent) variables. SEM is a general framework that involves simultaneously solving systems of linear equations and encompasses other techniques such as regression, factor analysis, path analysis, and latent growth curve modeling. Recently, SEM has gained popularity in the analysis of complex genetic traits because it can be used to better analyze the relationships between correlated variables (traits), to model genes as latent variables as a function of multiple observed genetic variants, and to assess the association between multiple genetic variants and multiple correlated phenotypes of interest. Though the general SEM framework only allows for the analysis of independent observations, recent work has extended SEM for the analysis of data on general pedigrees. Here, we review the theory of SEM for both unrelated and family data, describe the available software for SEM, and provide examples of SEM analysis.

Structural Equation Modeling

Statistical Analysis with Missing Data

This paper investigates the relationship between organizational aging and innovation processes to illuminate the dynamics of high-technology industries, as well to resolve debates in organizational...

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Aging, Obsolescence, and Organizational Innovation:

Part I. Causality and Empirical Research in the Social Sciences: 1. Introduction Part II. Counterfactuals, Potential Outcomes, and Causal Graphs: 2. Counterfactuals and the potential-outcome model 3. Causal graphs Part III. Estimating Causal Effects by Conditioning on Observed Variables to Block Backdoor Paths: 4. Models of causal exposure and identification criteria for conditioning estimators 5. Matching estimators of causal effects 6. Regression estimators of causal effects 7. Weighted regression estimators of causal effects Part IV. Estimating Causal Effects When Backdoor Conditioning Is Ineffective: 8. Self-selection, heterogeneity, and causal graphs 9. Instrumental-variable estimators of causal effects 10. Mechanisms and causal explanation 11. Repeated observations and the estimation of causal effects Part V. Estimation When Causal Effects Are Not Point Identified by Observables: 12. Distributional assumptions, set identification, and sensitivity analysis Part VI. Conclusions: 13. Counterfactuals and the future of empirical research in observational social science.

Counterfactuals and Causal Inference: Methods and Principles for Social Research

Casual Inference in the Social and Behavioral Sciences. Missing Data. Specification and Estimation of Mean Structures. The Analysis of Contingency Tables. Latent Class Models. Panel Analysis for Metric Data. Panel Analysis for Qualitative Variables. Analysis of Event Histories. Random Coefficient Models. Index.

Handbook of statistical modeling for the social and behavioral sciences

Nonlinear latent variable models are specified that include quadratic forms and interactions of latent regressor variables as special cases. To estimate the parameters, the models are put in a Bayesian framework with conjugate priors for the parameters. The posterior distributions of the parameters and the latent variables are estimated using Markov chain Monte Carlo methods such as the Gibbs sampler and the Metropolis-Hastings algorithm. The proposed estimation methods are illustrated by two simulation studies and by the estimation of a non-linear model for the dependence of performance on task complexity and goal specificity using empirical data.

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A Bayesian Approach to Nonlinear Latent Variable Models Using the Gibbs Sampler and the Metropolis-Hastings Algorithm.

Models and parameters of finite mixtures of multivariate normal densities conditional on regressor variables are specified and estimated. We consider mixtures of multivariate normals where the expected value for each component depends on possibly nonnormal regressor variables. The expected values and covariance matrices of the mixture components are parameterized using conditional mean- and covariance-structures. We discuss the construction of the likelihood function, estimation of the mixture model with regressors using three different EM algorithms, estimation of the asymptotic covariance matrix of parameters and testing for the number of mixture components. In addition to simulation studies, data on food preferences are analyzed.

Mixtures of conditional mean- and covariance-structure models

Consumer credit scoring is often considered a classification task where clients receive either a good or a bad credit status. Default probabilities provide more detailed information about the creditworthiness of consumers, and they are usually estimated by logistic regression. Here, we present a general framework for estimating individual consumer credit risks by use of machine learning methods. Since a probability is an expected value, all nonparametric regression approaches which are consistent for the mean are consistent for the probability estimation problem. Among others, random forests (RF), k-nearest neighbors (kNN), and bagged k-nearest neighbors (bNN) belong to this class of consistent nonparametric regression approaches. We apply the machine learning methods and an optimized logistic regression to a large dataset of complete payment histories of short-termed installment credits. We demonstrate probability estimation in Random Jungle, an RF package written in C++ with a generalized framework for fast tree growing, probability estimation, and classification. We also describe an algorithm for tuning the terminal node size for probability estimation. We demonstrate that regression RF outperforms the optimized logistic regression model, kNN, and bNN on the test data of the short-term installment credits.

Consumer credit risk: Individual probability estimates using machine learning

Three different discriminant techniques are applied and compared to analyze a complex data set of credit risks. A large sample is split into a training, a validation, and a test sample. The dependent variable is whether a loan is paid back without problems or not. Predictor variables are sex, job duration, age, car ownership, telephone ownership, and marital status. The statistical techniques are logistic discriminant analysis with a simple mean effects model, classification tree analysis, and a feedforward network with one hidden layer consisting of three units. It turns out, that in the given test sample, the predictive power is about equal for all techniques with the logistic discrimination as the best technique. However, the feedforward network produces different classification rules from the logistic discrimination and the classification tree analysis. Therefore, an additional coupling procedure for forecasts is applied to produce a combined forecast. However, this forecast turns out to be slightly worse than the logit model.

Gerhard Arminger

Papers

Handbook of statistical modeling for the social and behavioral sciences

A Bayesian Approach to Nonlinear Latent Variable Models Using the Gibbs Sampler and the Metropolis-Hastings Algorithm.

Mixtures of conditional mean- and covariance-structure models

Consumer credit risk: Individual probability estimates using machine learning

Analyzing Credit Risk Data: A Comparison of Logistic Discrimination, Classification Tree Analysis, and Feedforward Networks