Psychometrika最新文献

The deployment of statistical models-such as those used in item response theory-necessitates the use of indices that are informative about the degree to which a given model is appropriate for a specific data context. We introduce the InterModel Vigorish (IMV) as an index that can be used to quantify accuracy for models of dichotomous item responses based on the improvement across two sets of predictions (i.e., predictions from two item response models or predictions from a single such model relative to prediction based on the mean). This index has a range of desirable features: It can be used for the comparison of non-nested models and its values are highly portable and generalizable. We use this fact to compare predictive performance across a variety of simulated data contexts and also demonstrate qualitative differences in behavior between the IMV and other common indices (e.g., the AIC and RMSEA). We also illustrate the utility of the IMV in empirical applications with data from 89 dichotomous item response datasets. These empirical applications help illustrate how the IMV can be used in practice and substantiate our claims regarding various aspects of model performance. These findings indicate that the IMV may be a useful indicator in psychometrics, especially as it allows for easy comparison of predictions across a variety of contexts.

Mediation analysis plays an important role in understanding causal processes in social and behavioral sciences. While path analysis with composite scores was criticized to yield biased parameter estimates when variables contain measurement errors, recent literature has pointed out that the population values of parameters of latent-variable models are determined by the subjectively assigned scales of the latent variables. Thus, conclusions in existing studies comparing structural equation modeling (SEM) and path analysis with weighted composites (PAWC) on the accuracy and precision of the estimates of the indirect effect in mediation analysis have little validity. Instead of comparing the size on estimates of the indirect effect between SEM and PAWC, this article compares parameter estimates by signal-to-noise ratio (SNR), which does not depend on the metrics of the latent variables once the anchors of the latent variables are determined. Results show that PAWC yields greater SNR than SEM in estimating and testing the indirect effect even when measurement errors exist. In particular, path analysis via factor scores almost always yields greater SNRs than SEM. Mediation analysis with equally weighted composites (EWCs) also more likely yields greater SNRs than SEM. Consequently, PAWC is statistically more efficient and more powerful than SEM in conducting mediation analysis in empirical research. The article also further studies conditions that cause SEM to have smaller SNRs, and results indicate that the advantage of PAWC becomes more obvious when there is a strong relationship between the predictor and the mediator, whereas the size of the prediction error in the mediator adversely affects the performance of the PAWC methodology. Results of a real-data example also support the conclusions.

When surveys contain direct questions about sensitive topics, participants may not provide their true answers. Indirect question techniques incentivize truthful answers by concealing participants' responses in various ways. The Crosswise Model aims to do this by pairing a sensitive target item with a non-sensitive baseline item, and only asking participants to indicate whether their responses to the two items are the same or different. Selection of the baseline item is crucial to guarantee participants' perceived and actual privacy and to enable reliable estimates of the sensitive trait. This research makes the following contributions. First, it describes an integrated methodology to select the baseline item, based on conceptual and statistical considerations. The resulting methodology distinguishes four statistical models. Second, it proposes novel Bayesian estimation methods to implement these models. Third, it shows that the new models introduced here improve efficiency over common applications of the Crosswise Model and may relax the required statistical assumptions. These three contributions facilitate applying the methodology in a variety of settings. An empirical application on attitudes toward LGBT issues shows the potential of the Crosswise Model. An interactive app, Python and MATLAB codes support broader adoption of the model.

This paper proposes a method for assessing differential item functioning (DIF) in item response theory (IRT) models. The method does not require pre-specification of anchor items, which is its main virtue. It is developed in two main steps: first by showing how DIF can be re-formulated as a problem of outlier detection in IRT-based scaling and then tackling the latter using methods from robust statistics. The proposal is a redescending M-estimator of IRT scaling parameters that is tuned to flag items with DIF at the desired asymptotic type I error rate. Theoretical results describe the efficiency of the estimator in the absence of DIF and its robustness in the presence of DIF. Simulation studies show that the proposed method compares favorably to currently available approaches for DIF detection, and a real data example illustrates its application in a research context where pre-specification of anchor items is infeasible. The focus of the paper is the two-parameter logistic model in two independent groups, with extensions to other settings considered in the conclusion.

Wu and Browne (Psychometrika 80(3):571-600, 2015. https://doi.org/10.1007/s11336-015-9451-3 ; henceforth W &B) introduced the notion of adventitious error to explicitly take into account approximate goodness of fit of covariance structure models (CSMs). Adventitious error supposes that observed covariance matrices are not directly sampled from a theoretical population covariance matrix but from an operational population covariance matrix. This operational matrix is randomly distorted from the theoretical matrix due to differences in study implementations. W &B showed how adventitious error is linked to the root mean square error of approximation (RMSEA) and how the standard errors (SEs) of parameter estimates are augmented. Our contribution is to consider adventitious error as a general phenomenon and to illustrate its consequences. Using simulations, we illustrate that its impact on SEs can be generalized to pairwise relations between variables beyond the CSM context. Using derivations, we conjecture that heterogeneity of effect sizes across studies and overestimation of statistical power can both be interpreted as stemming from adventitious error. We also show that adventitious error, if it occurs, has an impact on the uncertainty of composite measurement outcomes such as factor scores and summed scores. The results of a simulation study show that the impact on measurement uncertainty is rather small although larger for factor scores than for summed scores. Adventitious error is an assumption about the data generating mechanism; the notion offers a statistical framework for understanding a broad range of phenomena, including approximate fit, varying research findings, heterogeneity of effects, and overestimates of power.

We aim to estimate school value-added dynamically in time. Our principal motivation for doing so is to establish school effectiveness persistence while taking into account the temporal dependence that typically exists in school performance from one year to the next. We propose two methods of incorporating temporal dependence in value-added models. In the first we model the random school effects that are commonly present in value-added models with an auto-regressive process. In the second approach, we incorporate dependence in value-added estimators by modeling the performance of one cohort based on the previous cohort's performance. An identification analysis allows us to make explicit the meaning of the corresponding value-added indicators: based on these meanings, we show that each model is useful for monitoring specific aspects of school persistence. Furthermore, we carefully detail how value-added can be estimated over time. We show through simulations that ignoring temporal dependence when it exists results in diminished efficiency in value-added estimation while incorporating it results in improved estimation (even when temporal dependence is weak). Finally, we illustrate the methodology by considering two cohorts from Chile's national standardized test in mathematics.

Multidimensional item response theory (MIRT) models have generated increasing interest in the psychometrics literature. Efficient approaches for estimating MIRT models with dichotomous responses have been developed, but constructing an equally efficient and robust algorithm for polytomous models has received limited attention. To address this gap, this paper presents a novel Gaussian variational estimation algorithm for the multidimensional generalized partial credit model. The proposed algorithm demonstrates both fast and accurate performance, as illustrated through a series of simulation studies and two real data analyses.