Bias for Treatment Effect by Measurement Error in Pretest in ANCOVA Analysis

This paper investigated consequences of measurement error in the pretest on the estimate of the treatment effect in a pretest–posttest design with the analysis of covariance (ANCOVA) model, focusing on both the direction and magnitude of its bias. Some prior studies have examined the magnitude of the bias due to measurement error and suggested ways to correct it. However, none of them clarified how the direction of bias is affected by measurement error. This study analytically derived a formula for the asymptotic bias for the treatment effect. The derived formula is a function of the reliability of the pretest, the standardized population group mean difference for the pretest, and the correlation between pretest and posttest true scores. It revealed a concerning consequence of ignoring measurement errors in pretest scores: treatment effects could be overestimated or underestimated, and positive treatment effects can be estimated as negative effects in certain conditions. A simulation study was also conducted to verify the derived bias formula.

A Test Can Have Multiple Reliabilities

It is argued that the generalizability theory interpretation of coefficient alpha is important. In this interpretation, alpha is a slightly biased but consistent estimate for the coefficient of generalizability in a subjects x items design where both subjects and items are randomly sampled. This interpretation is based on the “domain sampling” true scores. It is argued that these true scores have a more solid empirical basis than the true scores of Lord and Novick (1968), which are based on “stochastic subjects” (Holland, 1990), while only a single observation is available for each within-subject distribution. Therefore, the generalizability interpretation of coefficient alpha is to be preferred, unless the true scores can be defined by a latent variable model that has undisputed empirical validity for the test and that is sufficiently restrictive to entail a consistent estimate of the reliability—as, for example, McDonald’s omega. If this model implies that the items are essentially tau-equivalent, both the generalizability and the reliability interpretation of alpha can be defensible.

The Misreporting Trade-Off Between List Experiments and Direct Questions in Practice: Partition Validation Evidence from Two Countries

To reduce strategic misreporting on sensitive topics, survey researchers increasingly use list experiments rather than direct questions. However, the complexity of list experiments may increase nonstrategic misreporting. We provide the first empirical assessment of this trade-off between strategic and nonstrategic misreporting. We field list experiments on election turnout in two different countries, collecting measures of respondents’ true turnout. We detail and apply a partition validation method which uses true scores to distinguish true and false positives and negatives for list experiments, thus allowing detection of nonstrategic reporting errors. For both list experiments, partition validation reveals nonstrategic misreporting that is: undetected by standard diagnostics or validation; greater than assumed in extant simulation studies; and severe enough that direct turnout questions subject to strategic misreporting exhibit lower overall reporting error. We discuss how our results can inform the choice between list experiment and direct question for other topics and survey contexts.

Correcting the Correction: A Revised Formula to Estimate Partial Correlations between True Scores

Bohrnstedt’s (1969) attempt to derive a formula to compute the partial correlation coefficient and simultaneously correct for attenuation sought to simplify the process of performing each task separately. He suggested that his formula, developed from algebraic and psychometric manipulations of the partial correlation coefficient, produces a corrected partial correlation value. However, an algebraic error exists within his derivations. Consequently, the formula proposed by Bohrnstedt does not appropriately represent the value he intended it to estimate. By correcting the erroneous step and continuing the derivation based upon his proposed procedure, the steps outlined in this paper ultimately produce the formula that Bohrnstedt desired.

Nonparametric Item Response Models: A Comparison on Recovering True Scores

Nonparametric procedures are used to add flexibility to models. Three nonparametric item response models have been proposed, but not directly compared: the Kernel smoothing (KS-IRT); the Davidian-Curve (DC-IRT); and the Bayesian semiparametric Rasch model (SP-Rasch). The main aim of the present study is to compare the performance of these procedures in recovering simulated true scores, using sum scores as benchmarks. The secondary aim is to compare their performances in terms of practical equivalence with real data. Overall, the results show that, apart from the DC-IRT, which is the model that performs the worse, all the other models give results quite similar to those when sum scores are used. These results are followed by a discussion with practical implications and recommendations for future studies.

Situational optimization function analysis: An ideal performance analysis inspired on Lewin’s Equation

This study presents the situational optimization function analysis (SOFA) and has three aims. First, to develop a Bayesian implementation of SOFA. Second, to compare this implementation with three other maximum likelihood-based models in their accuracy to estimate true scores. The third aim is to show how joint modeling can be used for validity research. A simulation study was used to examine the second aim, while an empirical example was used to illustrate the third aim. The simulation study used three data generating processes, with varying degrees of deviation from linear models and with different sample sizes. Results of the simulation study showed that the Bayesian implementation supersedes the other models. In the empirical example, data collected from 66 participants using an iterated prisoner dilemma and a scale measuring cooperation-competition attitudes were used. Results showed that joint modeling is the best fitting model, also increasing the correlation between the true scores of both measures (deviations from the iterated prisoner dilemma and the scale). Finally, implications, limitations and future studies are discussed.

Modeling of Item Response Functions Under the D-Scoring Method

This study presents new models for item response functions (IRFs) in the framework of the D-scoring method (DSM) that is gaining attention in the field of educational and psychological measurement and largescale assessments. In a previous work on DSM, the IRFs of binary items were estimated using a logistic regression model (LRM). However, the LRM underestimates the item true scores at the top end of the D-scale (ranging from 0 to 1), especially for relatively difficult items. This entails underestimation of true D-scores, inaccuracy in the estimates of their standard errors, and other psychometric issues. The inverse-regression adjustments used to fix this problem are too complicated for regular applications of the DSM and not in line with its simplicity. This issue is resolved with the IRF models proposed in this study, referred to as rational function models (RFMs) with one parameter (RFM1), two parameters (RFM2), and three parameters (RFM3). The proposed RFMs are discussed and illustrated with simulated and real data.