A simple and powerful test for autocorrelated errors in OLS intervention models

The important assumption of independent errors should be evaluated routinely in the application of interrupted time-series regression models. The two most frequently recommended tests of this assumption [Mood's runs test and the Durbin-Watson (D-W) bounds test] have several weaknesses. The former has poor small sample Type I error performance and the latter has the bothersome property that results are often declared to be "inconclusive." The test proposed in this article is simple to compute (special software is not required), there is no inconclusive region, an exact p-value is provided, and it has good Type I error and power properties relative to competing procedures. It is shown that these desirable properties hold when design matrices of a specified form are used to model the response variable. A Monte Carlo evaluation of the method, including comparisons with other tests (viz., runs, D-W bounds, and D-W beta), and examples of application are provided.     

An elicitation method for multiple linear regression models

This paper describes a method of quantifying subjective opinion about a normal linear regression model. Opinion about the regression coefficients and experimental error is elicited and modeled by a multivariate probability distribution (a Bayesian conjugate prior distribution). The distribution model is richly parameterized and various assessment tasks are used to estimate its parameters. These tasks include the revision of opinion in the light of hypothetical data, the assessment of credible intervals, and a task commonly performed in cue-weighting experiments. A new assessment task is also introduced. In addition, implementation of the method in an interactive computer program is described and the method is illustrated with a practical example.     

Graphical regression models for polytomous variables

When modeling the relationship between two nominal categorical variables, it is often desirable to include covariates to understand how individuals differ in their response behavior. Typically, however, not all the relevant covariates are available, with the result that the measured variables cannot fully account for the associations between the nominal variables. Under the assumption that the observed and unobserved variables follow a homogeneous conditional Gaussian distribution, this paper proposesRC(M) regression models to decompose the residual associations between the polytomous variables. Based on Goodman's (1979, 1985)RC(M) association model, a distinctive feature ofRC(M) regression models is that they facilitate the joint estimation of effects due to manifest and omitted (continuous) variables without requiring numerical integration. TheRC(M) regression models are illustrated using data from the High School and Beyond study (Tatsuoka & Lohnes, 1988). This article was accepted for publication, when Willem J. Heiser was the Editor ofPsychometrika. This research was supported by grants from the National Science Foundation (#SBR96-17510 and #SBR94-09531) and the Bureau of Educational Research at the University of Illinois. We thank Jee-Seon Kim for comments and computational assistance.     

An improved spatial span test of visuospatial memory

In the widely used Corsi Block Test and Wechsler Spatial Span Tests, participants must reproduce sequences of blocks in the order touched by the examiner until two trials are missed at the same sequence length. The examiner records either the maximum number of blocks correctly reported or the total number of correct lists. Here, we describe a computerized spatial span test (C-SST) that uses psychophysical procedures to quantify visuospatial mean span (MnS) with sub-digit precision. Results from 187 participants ranging in age from 18 to 82 years showed that accuracy declined gradually with list length around the MnS (by ～30% per item). Simulation studies revealed high variance and biases in CBT and Wechsler measures, and demonstrated that the C-SST provided the most accurate estimate of true span (i.e., the sequence length producing 50% correct). MnS declined more rapidly with age than mean digit span (MnDS) measured in the same participants. Response times correlated with both MnS and MnDS scores. Error analysis showed that omission and transposition errors predominated, with weaker primacy and recency effects in spatial span than digit span testing. The C-SST improves the precision of spatial span testing and reveals significant differences between visuospatial and verbal working memory.     

An empirical test of two psychophysical models

Two theoretical relationships between sensitivity measures (Weber fractions, Ekman fractions, and their logarithms) and the exponents of the psychophysical power function were tested empirically with the brightness attribute. One model was based on Weber and Ekman fractions, the other on the logarithms of these measures. The stimulus parameters were time interval between standard and comparison targets and position of the standard in the luminance series. Weber fractions were based on data obtained by the method of constant stimuli, whereas Ekman fractions and exponents were based on data obtained by magnitude estimation. The results were in closer agreement with the theoretical predictions generated by the logarithmic model when group data were analyzed. With individual subjects, a detailed correspondence between fact and theory was not found with either model.     

Estimating standard errors in feature network models

Feature network models are graphical structures that represent proximity data in a discrete space while using the same formalism that is the basis of least squares methods employed in multidimensional scaling. Existing methods to derive a network model from empirical data only give the best‐fitting network and yield no standard errors for the parameter estimates. The additivity properties of networks make it possible to consider the model as a univariate (multiple) linear regression problem with positivity restrictions on the parameters. In the present study, both theoretical and empirical standard errors are obtained for the constrained regression parameters of a network model with known features. The performance of both types of standard error is evaluated using Monte Carlo techniques.     

Experimental manipulations of responsibility: An analogue test for models of Obsessive-Compulsive Disorder

Several authors attribute excessive responsibility a predominant role in Obsessive-Compulsive Disorder (OCD) [Salkovskis, P. M. (1985) Behaviour Research and Therapy, 23, 571–583; Rachman, S. (1993) Behaviour Research and Therapy, 31, 149–154; van Oppen, P. & Arntz, A. (1994) Behaviour Research and Therapy, 32, 79–87]. The present studies aimed at demonstrating the link between different levels of perceived responsibility and checking behaviors by experimentally manipulating responsibility in non-clinical Ss. In the first study, a sound recognition task was used to compare checking behaviors in Ss with high (HR) and low (LR) perceived responsibility. Only one variable was significantly different, Ss from the HR group reporting more anxiety during the task than Ss from the LR group. Results did not support a link between responsibility and checking behavior. In a second study HR and LR Ss were compared on a manual classification task. Subjects from the HR group hesitated and checked more, and reported more preoccupation with errors and anxiety during the task than Ss from the LR group. Since perceived severity of the outcome was the most variable affected by the manipulation, the implications for current models of OCD are discussed and an alternative explanation is attempted. Finally, clinical implications are examined and suggestions are made for future directions of research.     

An empirical study of the normality and independence of errors of measurement in test scores

An empirical study of test scores shows the variance of the errors of measurement to be significantly associated with true score in each of four groups studied; it also shows the distribution of the errors of measurement to be significantly skewed in three of these four groups. The mathematical rationale underlying the statistical treatment is presented. Standard error formulas are given for making the necessary significance tests.This research was in part carried out under Contracts Nonr-2214(00) and Nonr-2752(00) with the Office of Naval Research, Department of the Navy.     

Two-sample models with monotonic likelihood ratios for ordinal regression

Signal detection experiments with human observers frequently generate ordinal data which are evaluated using receiver operating characteristic (ROC) methods. These methods may include regressing a continuous two-distribution model to the data set. Because we assume that human observers will not systematically select observations absent the signal, this model should have a monotonic likelihood ratio between the distributions. This paper gives a general method for constructing pairs of distributions that have monotonic likelihood ratios and a possibly large number flexible parameters. It suggests two specific simple parametric forms of monotonic likelihood ratios, constructs new distributions with those likelihood ratios using other standard distributions, and performs ordinal regression with those new distributions to model some example data from the literature.     

An improved method for tetrachoricr

From the ratio of the cross-products of a fourfold table, with the application of two tabled corrections, tetrachoricr's can be estimated with a mean discrepancy of less than .005 even when splits vary greatly from the medians. The necessary calculations can be handled by slide rule and the correction tables used without interpolation.     

A test of inclusion which allows for errors of measurement

A test which allows for errors of measurement is derived for the hypothesis that all the members of a population who possess a certain skill are a sub-set of the members who possess another skill. Formulae are given for one particular case when two questions are used for each skill, and for when three questions are used for each skill. An illustrative example is given for the two-question case. The authors are indebted to M. L. Turner for his assistance in the initial stages of development of the test.     

Bayesian Gaussian distributional regression models for more efficient norm estimation

A test score on a psychological test is usually expressed as a normed score, representing its position relative to test scores in a reference population. These typically depend on predictor(s) such as age. The test score distribution conditional on predictors is estimated using regression, which may need large normative samples to estimate the relationships between the predictor(s) and the distribution characteristics properly. In this study, we examine to what extent this burden can be alleviated by using prior information in the estimation of new norms with Bayesian Gaussian distributional regression. In a simulation study, we investigate to what extent this norm estimation is more efficient and how robust it is to prior model deviations. We varied the prior type, prior misspecification and sample size. In our simulated conditions, using a fixed effects prior resulted in more efficient norm estimation than a weakly informative prior as long as the prior misspecification was not age dependent. With the proposed method and reasonable prior information, the same norm precision can be achieved with a smaller normative sample, at least in empirical problems similar to our simulated conditions. This may help test developers to achieve cost-efficient high-quality norms. The method is illustrated using empirical normative data from the IDS-2 intelligence test.     

A model-based approach to multivariate principal component regression: Selecting principal components and estimating standard errors for unstandardized regression coefficients

Principal component regression (PCR) is a popular technique in data analysis and machine learning. However, the technique has two limitations. First, the principal components (PCs) with the largest variances may not be relevant to the outcome variables. Second, the lack of standard error estimates for the unstandardized regression coefficients makes it hard to interpret the results. To address these two limitations, we propose a model-based approach that includes two mean and covariance structure models defined for multivariate PCR. By estimating the defined models, we can obtain inferential information that will allow us to test the explanatory power of individual PCs and compute the standard error estimates for the unstandardized regression coefficients. A real example is used to illustrate our approach, and simulation studies under normality and nonnormality conditions are presented to validate the standard error estimates for the unstandardized regression coefficients. Finally, future research topics are discussed.     

An individual differences model for multiple regression

A model for multiple regression was developed which allows individual differences to emerge empirically. The model encompasses as special cases several of the previous attempts to improve psychological prediction by deviating from the usual linear multiple regression model. The model is tested with both artificial and real data. The results indicate that the model effectively reduces the variance of the error of prediction, and that the weights obtained are stable over different samples, and, to some extent, over different sets of predictors.This article is based upon a thesis submitted in partial fulfillment of the requirements for the doctoral degree at the University of Illinois. The author thanks Professor Ledyard R Tucker who served as committee chairman and offered considerable support and assistance.