Estimation of true score and error variance for tests under various equivalence assumptions

Maximum-likelihood estimators of true score variance and error variance for mental tests are derived for six different models of equivalent measurements. Statistical properties of the estimators are examined. Main emphasis is placed upon essentially-equivalent measurements. A statistical criterion for this type of measurement is given. The solution of the comparatively simple maximum-likelihood equations is effected by means of a rapid Newton-Raphson procedure. Two different initial estimators are considered and their relative merits in terms of second moments evaluated. Four numerical examples are appended by way of illustration.Paper read at the Mathematical Psychology Meeting, August 28, 1968, at Stanford, Calfornia.This research was supported in part by the National Institute of Child Health and Human Development, Research Grant 1 P01 HD01762.     

The statistical theory of stepped-up reliability coefficients when a test has been divided into several equivalent parts

This paper is a presentation of the statistical sampling theory of stepped-up reliability coefficients when a test has been divided into any number of equivalent parts. Maximum-likelihood estimators of the reliability are obtained and shown to be biased. Their sampling distributions are derived and form the basis of the definition of new unbiased estimators with known sampling distributions. These unbiased estimators have a smaller sampling variance than the maximum-likelihood estimators and are, because of this and some other favorable properties, recommended for general use. On the basis of the variances of the unbiased estimators the gain in accuracy in estimating reliability connected with further division of a test can be expressed explicitly. The limits of these variances and thus the limits of accuracy of estimation are derived. Finally, statistical small sample tests of the reliability coefficient are outlined. This paper also covers the sampling distribution of Cronbach's coefficient alpha.     

Flexible Mediation Analysis in the Presence of Nonlinear Relations: Beyond the Mediation Formula

In the social sciences, mediation analysis has typically been formulated in the context of linear models using the Baron &; Kenny (1986) Baron, R. M. and Kenny, D. A. 1986. The moderator-mediator variable distinction in social psychological research: Conceptual, strategic and statistical considerations. Journal of Personality and Social Psychology, 51: 1173–1182. [Crossref], [PubMed], [Web of Science ®] , [Google Scholar] approach. Extensions to nonlinear models have been considered but lack formal justification. By placing mediation analysis within the counterfactual framework of causal inference one can define causal mediation effects in a way that is not tied to a specific statistical model and identify them under certain no unmeasured confounding assumptions. Corresponding estimation procedures using parametric or nonparametric models, based on the so-called mediation formula, have recently been proposed in the psychological literature and made accessible through the R-package mediation. A number of limitations of the latter approach are discussed and a more flexible approach using natural effects models is proposed as an alternative. The latter builds on the same counterfactual framework but enables interpretable and parsimonious modeling of direct and mediated effects and facilitates tests of hypotheses that would otherwise be difficult or impossible to test. We illustrate the approach in a study of individuals who ended a romantic relationship and explore whether the effect of attachment anxiety during the relationship on unwanted pursuit behavior after the breakup is mediated by negative affect during the breakup.     

The temporal dynamics of first versus second language production

In this study we explored the temporal origin of processing differences between first and second language production. Forty highly proficient bilinguals named objects of high and low lexical frequency aloud for both L1 and L2 separately while event-related brain potentials (ERPs) were recorded. The first electrophysiological differences elicited by response language occurred at the same early P2 peak (∼140–220 ms) where we observed the onset of the lexical frequency effect, but only for those bilinguals who started naming in an L1 context and afterwards switched to an L2 naming context. The bilinguals who named objects in the reverse direction did not display a language effect in the ERPs. Taken together, the data show that the L2 naming disadvantage originates during the onset of lexical access and seems to be driven by both representational strength, which is lower for L2 words, and language control demands, which are higher for L2 words.     

Testing a linear relation between true scores of two measures

We concern ourselves with the hypothesis that two variables have a perfect disattenuated correlation, hence measure the same trait except for errors of measurement. This hypothesis is equivalent to saying, within the adopted model, that true scores of two psychological tests satisfy a perfect linear relation. Statistical tests of this hypothesis are derived when the relation is specified with the exception of the additive constant. Two approaches are presented and various assumptions concerning the error parameters are used. Then the results are reinterpreted in terms of the possible existence of an unspecified perfect linear relation between true scores of two psychological tests. A numerical example is appended by way of illustration. Research reported in this paper has been supported by grant GB-18230 from National Science Foundation.     

On the theory of a set of tests which differ only in length

This paper presents a contribution to the sampling theory of a set of homogeneous tests which differ only in length, test length being regarded as an essential test parameter. Observed variance-covariance matrices of such measurements are taken to follow a Wishart distribution. The familiar true score-and-error concept of classical test theory is employed. Upon formulation of the basic model it is shown that in a combination of such tests forming a “total” test, the singal-to-noise ratio of the components is additive and that the inverse of the population variance-covariance matrix of the component measures has all of its off-diagonal elements equal, regardless of distributional assumptions. This fact facilitates the subsequent derivation of a statistical sampling theory, there being at mostm + 1 free parameters whenm is the number of component tests. In developing the theory, the cases of known and unknown test lengths are treated separately. For both cases maximum-likelihood estimators of the relevant parameters are derived. It is argued that the resulting formulas will remain resonable even if the distributional assumptions are too narrow. Under these assumptions, however, maximum-likelihood ratio tests of the validity of the model and of hypotheses concerning reliability and standard error of measurement of the total test are given. It is shown in each case that the maximum-likelihood equations possess precisely one acceptable solution under rather natural conditions. Application of the methods can be effected without the use of a computer. Two numerical examples are appended by way of illustration. This research was supported in part by The National Institute of Child Health and Human Development, under Research Grant 1 PO1 HDO1762.     

On accuracy in reliability estimation

This study in parametric test theory deals with the statistics of reliability estimation when scores on two parts of a test follow a binormal distribution with equal (Case 1) or unequal (Case 2) expectations. In each case biased maximum-likelihood estimators of reliability are obtained and converted into unbiased estimators. Sampling distributions are derived. Second moments are obtained and utilized in calculating mean square errors of estimation as a measure of accuracy. A rank order of four estimators is established. There is a uniformly best estimator. Tables of absolute and relative accuracies are provided for various reliability parameters and sample sizes.     

Time-Varying Treatments in Observational Studies: Marginal Structural Models of the Effects of Early Grade Retention on Math Achievement

One of the main objectives of many empirical studies in the social and behavioral sciences is to assess the causal effect of a treatment or intervention on the occurrence of a certain event. The randomized controlled trial is generally considered the gold standard to evaluate such causal effects. However, for ethical or practical reasons, social scientists are often bound to the use of nonexperimental, observational designs. When the treatment and control group are different with regard to variables that are related to the outcome, this may induce the problem of confounding. A variety of statistical techniques, such as regression, matching, and subclassification, is now available and routinely used to adjust for confounding due to measured variables. However, these techniques are not appropriate for dealing with time-varying confounding, which arises in situations where the treatment or intervention can be received at multiple timepoints. In this article, we explain the use of marginal structural models and inverse probability weighting to control for time-varying confounding in observational studies. We illustrate the approach with an empirical example of grade retention effects on mathematics development throughout primary school.     

Common Ideological Roots of Speciesism and Generalized Ethnic Prejudice: The Social Dominance Human–Animal Relations Model (SD‐HARM)

Recent research and theorizing suggest that desires for group‐based dominance underpin biases towards both human outgroups and (non‐human) animals. A systematic study of the common ideological roots of human–human and human–animal biases is, however, lacking. Three studies (in Belgium, UK, and USA) tested the Social Dominance Human–Animal Relations Model (SD‐HARM) proposing that Social Dominance Orientation (SDO) is a key factor responsible for the significant positive association between ethnic outgroup attitudes and speciesist attitudes towards animals, even after accounting for other ideological variables (that possibly confound previous findings). Confirming our hypotheses, the results consistently demonstrated that SDO, more than right‐wing authoritarianism (RWA), is a key factor connecting ethnic prejudice and speciesist attitudes. Furthermore, Studies 2 and 3 showed that both SDO and RWA are significantly related to perceived threat posed by vegetarianism (i.e. ideologies and diets minimizing harm to animals), but with SDO playing a focal role in explaining the positive association between threat perceptions and ethnic prejudice. Study 3 replicated this pattern, additionally including political conservatism in the model, itself a significant correlate of speciesism. Finally, a meta‐analytic integration across studies provided robust support for SD‐HARM and offers important insights into the psychological parallels between human intergroup and human–animal relations. Copyright © 2016 European Association of Personality Psychology