Linear functional relationships are intended to be symmetric and therefore cannot generally be accurately estimated using ordinary least squares regression equations. Orthogonal regression (OR) models allow for errors in both "Y" and "X" and therefore can provide symmetric estimates of these relationships. The most…

It is common in regression discontinuity analysis to control for high order (third, fourth, or higher) polynomials of the forcing variable. We argue that estimators for causal effects based on such methods can be misleading, and we recommend researchers do not use them, and instead use estimators based on local linear or quadratic polynomials or…

Propensity score analysis (PSA) is a methodological technique which may correct for selection bias in a quasi-experiment by modeling the selection process using observed covariates. Because logistic regression is well understood by researchers in a variety of fields and easy to implement in a number of popular software packages, it has…

The relationship between complexity and usefulness can be captured by a U-shaped curve. This comment explores that relationship. Complexity may be useful for one of the main aims of developmental psychology (causal inference) but not for another (description of developmental phenomena). Currently, developmentalists conduct complex analyses that…

A two-stage generalized least squares model is developed for estimating the linear regression of an individual outcome on a group characteristic in studies of multilevel data. Results of this model are compared to the results of analytic methods, and formulas are developed for assessing the accuracy of the traditional approaches. (Author/JAZ)

Monte Carlo techniques were used to examine regression approaches to external unfolding. The present analysis examined the technique to determine if various characteristics of the points are recovered (such as ideal points). Generally, monotonic analyses resulted in good recovery. (TJH)

Psychometricians working in factor analysis and econometricians working in regression with measurement error in all variables are both interested in the rank of dispersion matrices under variation of diagonal elements. This paper reviews both fields; points out various small errors; and presents a methodological comparision of factor analysis and…

Some approximate formulas are presented for standard errors of estimated regression coefficients in two-level designs. If the researcher can make a reasonable guess as to parameters occurring in the model, this approximation can be a guide to the choice of sample sizes at either level. (SLD)

Regression to the mean (RTM) is often misunderstood. It is demonstrated that artifactual RTM depends fundamentally on the magnitude of measurement error at pretest. Adjustment usually involves estimating the measurement error and determining consequences, but even without adjustment, effects of RTM can be ameliorated. (SLD)

The importance of regression diagnostics in detecting influential data points is discussed, and five statistics are recommended for the applied researcher. The suggested diagnostics were used on a dataset of 24 subjects, and effects were analyzed. Colinearity-based diagnostics and diagnostics for a variety of procedures are discussed. (SLD)

An analysis of covariance (ANCOVA) is done to correct for chance differences that occur when subjects are assigned randomly to treatment groups. When properly used, this correction results in adjustment of the group means for pre-existing differences caused by sampling error and reduction of the size of the error variance of the analysis. The…

In research, data sets often occur in which the variance of the distribution of the dependent variable at given levels of the predictors is a function of the values of the predictors. In this situation, the use of weighted least-squares (WLS) or techniques is required. Weights suitable for use in a WLS regression analysis must be estimated. A…

A well-established approach to modeling clustered data introduces random effects in the model of interest. Mixed-effects logistic regression models can be used to predict discrete outcome variables when observations are correlated. An extension of the mixed-effects logistic regression model is presented in which the dependent variable is a latent…

Often, all of the variables in a model are latent, random, or subject to measurement error, or there is not an obvious dependent variable. When any of these conditions exist, an appropriate method for estimating the linear relationships among the variables is Least Principal Components Analysis. Least Principal Components are robust, consistent,…

A component analytic method for analyzing multivariate longitudinal data is presented that does not make strong assumptions about the structure of the data. Central to the method are the facts that components are derived as linear composites of the observed or manifest variables and that the components must provide an adequate representation of…