Political scientists regularly rely on a selection-on-observables assumption to identify causal effects of interest. Once a causal effect has been identified in this way, a wide variety of estimators can, in principle, be used to consistently estimate the effect of interest. While these estimators are all justified by appeals to the same causal identification assumptions, they often differ greatly in how they make use of the data at hand. For instance, methods based on regression rely on an explicit model of the outcome variable but do not explicitly model the treatment assignment process, whereas methods based on propensity scores explicitly model the treatment assignment process but do not explicitly model the outcome variable. Understanding the tradeoffs between estimation methods is complicated by these seemingly fundamental differences. In this paper we seek to rectify this problem. We do so by clarifying how most estimators of causal effects that are justified by an appeal to a selection-on-observables assumption are all special cases of a general weighting estimator. We then explain how this commonality provides for diagnostics that allow for meaningful comparisons across estimation methods—even when the methods are seemingly very different. We illustrate these ideas with two applied examples.

Factor score indeterminacy is a characteristic property of factor analysis (FA) models. This research introduces a novel procedure, regression-based factor score exploration (RFE), which uniquely determines factor scores and simultaneously estimates other parameters of the FA model. RFE uniquely determines factor scores by minimizing a loss function that balances FA and multivariate regression, regulated by a tuning parameter. Theoretical aspects of RFE, including the uniqueness of factor scores, the relationship between observed and latent variables, and rotational indeterminacy, are examined. Additionally, clustering-based factor exploration (CFE) is presented as a variant of RFE, derived by generalizing the penalty term to enable the clustering of factor scores. It is demonstrated that CFE creates cluster structures more accurately than the existing method. A simulation study shows that the proposed procedures accurately recover true parameter matrices even in the presence of error-contaminated data, with lower computational demand compared to existing methods. Real data examples illustrate that the proposed procedures provide interpretable results, demonstrating high relevance to the factor scores obtained by existing methods.

This paper uses a two-step approach to modelling the probability of a policyholder making an auto insurance claim. We perform clustering via Gaussian mixture models and cluster-specific binary regression models. We use telematics information along with traditional auto insurance information and find that the best model incorporates telematics, without the need for dimension reduction via principal components. We also utilise the probabilistic estimates from the mixture model to account for the uncertainty in the cluster assignments. The clustering process allows for the creation of driving profiles and offers a fairer method for policyholder segmentation than when clustering is not used. By fitting separate regression models to the observations from the respective clusters, we are able to offer differential pricing, which recognises that policyholders have different exposures to risk despite having similar covariate information, such as total miles driven. The approach outlined in this paper offers an explainable and interpretable model that can compete with black box models. Our comparisons are based on a synthesised telematics data set that was emulated from a real insurance data set.

Regression is a fundamental prediction task common in data-centric engineering applications that involves learning mappings between continuous variables. In many engineering applications (e.g., structural health monitoring), feature-label pairs used to learn such mappings are of limited availability, which hinders the effectiveness of traditional supervised machine learning approaches. This paper proposes a methodology for overcoming the issue of data scarcity by combining active learning (AL) for regression with hierarchical Bayesian modeling. AL is an approach for preferentially acquiring feature-label pairs in a resource-efficient manner. In particular, the current work adopts a risk-informed approach that leverages contextual information associated with regression-based engineering decision-making tasks (e.g., inspection and maintenance). Hierarchical Bayesian modeling allow multiple related regression tasks to be learned over a population, capturing local and global effects. The information sharing facilitated by this modeling approach means that information acquired for one engineering system can improve predictive performance across the population. The proposed methodology is demonstrated using an experimental case study. Specifically, multiple regressions are performed over a population of machining tools, where the quantity of interest is the surface roughness of the workpieces. An inspection and maintenance decision process is defined using these regression tasks, which is in turn used to construct the active-learning algorithm. The novel methodology proposed is benchmarked against an uninformed approach to label acquisition and independent modeling of the regression tasks. It is shown that the proposed approach has superior performance in terms of expected cost—maintaining predictive performance while reducing the number of inspections required.

Multivariate selection can be represented as a linear transformation in a geometric framework. This approach has led to considerable simplification in the study of the effects of selection on factor analysis. In this note this approach is extended to describe the effects of selection on regression analysis and to adjust for the effects of selection using the inverse of the linear transformation.

Bayesian least squares techniques are adapted to estimation of stimulus-response curves, rather broadly conceived. Illustrative examples deal with estimation of person characteristic curves and item characteristic curves in the context of mental testing, and estimation of a stimulus-response curve using data from a psychophysical experiment.

There is a unity underlying the diversity of models for the analysis of multivariate data. Essentially, they constitute a family models, most generally nonlinear, for structural/functional relations between variables drawn from a behavior domain.

This paper discusses least squares methods for fitting a reformulation of the general Euclidean model for the external analysis of preference data. The reformulated subject weights refer to a common set of reference vectors for all subjects and hence are comparable across subjects. If the rotation of the stimulus space is fixed, the subject weight estimates in the model are uniquely determined. Weight estimates can be guaranteed nonnegative. While the reformulation is a metric model for single stimulus data, the paper briefly discusses extensions to nonmetric, pairwise, and logistic models. The reformulated model is less general than Carroll's earlier formulation.

A summary and interpretation of the recent literature on the indeterminacy of factor scores is given in simple terms. A good index of factor score determinacy is the squared multiple correlation of the factor with the observed variables.

For analyses with missing data, some popular procedures delete cases with missing values, perform analysis with “missing value” correlation or covariance matrices, or estimate missing values by sample means. There are objections to each of these procedures. Several procedures are outlined here for replacing missing values by regression values obtained in various ways, and for adjusting coefficients (such as factor score coefficients) when data are missing. None of the procedures are complex or expensive.

Structural equation models with latent variables are sometimes estimated using an intuitive three-step approach, here denoted factor score regression. Consider a structural equation model composed of an explanatory latent variable and a response latent variable related by a structural parameter of scientific interest. In this simple example estimation of the structural parameter proceeds as follows: First, common factor models areseparately estimated for each latent variable. Second, factor scores areseparately assigned to each latent variable, based on the estimates. Third, ordinary linear regression analysis is performed among the factor scores producing an estimate for the structural parameter. We investigate the asymptotic and finite sample performance of different factor score regression methods for structural equation models with latent variables. It is demonstrated that the conventional approach to factor score regression performs very badly. Revised factor score regression, using Regression factor scores for the explanatory latent variables and Bartlett scores for the response latent variables, produces consistent estimators for all parameters.

In the current paper, we review existing tools for solving variable selection problems in psychology. Modern regularization methods such as lasso regression have recently been introduced in the field and are incorporated into popular methodologies, such as network analysis. However, several recognized limitations of lasso regularization may limit its suitability for psychological research. In this paper, we compare the properties of lasso approaches used for variable selection to Bayesian variable selection approaches. In particular we highlight advantages of stochastic search variable selection (SSVS), that make it well suited for variable selection applications in psychology. We demonstrate these advantages and contrast SSVS with lasso type penalization in an application to predict depression symptoms in a large sample and an accompanying simulation study. We investigate the effects of sample size, effect size, and patterns of correlation among predictors on rates of correct and false inclusion and bias in the estimates. SSVS as investigated here is reasonably computationally efficient and powerful to detect moderate effects in small sample sizes (or small effects in moderate sample sizes), while protecting against false inclusion and without over-penalizing true effects. We recommend SSVS as a flexible framework that is well-suited for the field, discuss limitations, and suggest directions for future development.

In the course of the medical program at the University of Limburg, students complete a total of 24 progress tests, consisting of items drawn from a constant itembank. A model is presented for the growth of knowledge reflected by these results. The Rasch model is used as a starting point, but both ability and difficulty parameters are taken to be random, and moreover the logistic distribution is replaced by the normal. Both individual and group abilities are estimated and explained through simple linear regression. Application to real data shows that the model fits very well.