The purpose of this note is to focus on the finiteness of the weighted likelihood estimator (WLE) of ability in the context of dichotomous and polytomous item response theory (IRT) models. It is established that the WLE always returns finite ability estimates. This general result is valid for dichotomous (one-, two-, three- and four-parameter logistic) IRT models, the class of polytomous difference models and divide-by-total models, independently of the number of items, the item parameters and the response patterns. Further implications of this result are outlined.

In a latent class IRT model in which the latent classes are ordered on one dimension, the class specific response probabilities are subject to inequality constraints. The number of these inequality constraints increase dramatically with the number of response categories per item, if assumptions like monotonicity or double monotonicity of the cumulative category response functions are postulated. A Markov chain Monte Carlo method, the Gibbs sampler, can sample from the multivariate posterior distribution of the parameters under the constraints. Bayesian model selection can be done by posterior predictive checks and Bayes factors. A simulation study is done to evaluate results of the application of these methods to ordered latent class models in three realistic situations. Also, an example of the presented methods is given for existing data with polytomous items. It can be concluded that the Bayesian estimation procedure can handle the inequality constraints on the parameters very well. However, the application of Bayesian model selection methods requires more research.

Item response curves for a set of binary responses are studied from a Bayesian viewpoint of estimating the item parameters. For the two-parameter logistic model with normally distributed ability, restricted bivariate beta priors are used to illustrate the computation of the posterior mode via the EM algorithm. The procedure is illustrated by data from a mathematics test.

This paper focuses on the computation of asymptotic standard errors (ASE) of ability estimators with dichotomous item response models. A general framework is considered, and ability estimators are defined from a very restricted set of assumptions and formulas. This approach encompasses most standard methods such as maximum likelihood, weighted likelihood, maximum a posteriori, and robust estimators. A general formula for the ASE is derived from the theory of M-estimation. Well-known results are found back as particular cases for the maximum and robust estimators, while new ASE proposals for the weighted likelihood and maximum a posteriori estimators are presented. These new formulas are compared to traditional ones by means of a simulation study under Rasch modeling.

A social network comprises both actors and the social connections among them. Such connections reflect the dependence among social actors, which is essential for individuals’ mental health and social development. In this article, we propose a mediation model with a social network as a mediator to investigate the potential mediation role of a social network. In the model, the dependence among actors is accounted for by a few mutually orthogonal latent dimensions which form a social space. The individuals’ positions in such a latent social space are directly involved in the mediation process between an independent and dependent variable. After showing that all the latent dimensions are equivalent in terms of their relationship to the social network and the meaning of each dimension is arbitrary, we propose to measure the whole mediation effect of a network. Although individuals’ positions in the latent space are not unique, we rigorously articulate that the proposed network mediation effect is still well defined. We use a Bayesian estimation method to estimate the model and evaluate its performance through an extensive simulation study under representative conditions. The usefulness of the network mediation model is demonstrated through an application to a college friendship network.

Intensive longitudinal data provide rich information, which is best captured when specialized models are used in the analysis. One of these models is the multilevel autoregressive model, which psychologists have applied successfully to study affect regulation as well as alcohol use. A limitation of this model is that the autoregressive parameter is treated as a fixed, trait-like property of a person. We argue that the autoregressive parameter may be state-dependent, for example, if the strength of affect regulation depends on the intensity of affect experienced. To allow such intra-individual variation, we propose a multilevel threshold autoregressive model. Using simulations, we show that this model can be used to detect state-dependent regulation with adequate power and Type I error. The potential of the new modeling approach is illustrated with two empirical applications that extend the basic model to address additional substantive research questions.

This article describes a Bayesian framework for estimation in item response models, with two-stage prior distributions on both item and examinee populations. Strategies for point and interval estimation are discussed, and a general procedure based on the EM algorithm is presented. Details are given for implementation under one-, two-, and three-parameter binary logistic IRT models. Novel features include minimally restrictive assumptions about examinee distributions and the exploitation of dependence among item parameters in a population of interest. Improved estimation in a moderately small sample is demonstrated with simulated data.

In very simple test theory models such as the Rasch model, a single parameter is used to represent the ability of any examinee or the difficulty of any item. Simple models such as these provide very important points of departure for more detailed modeling when a substantial amount of data are available, and are themselves of real practical value for small or even medium samples. They can also serve a normative role in test design.

As an alternative to the Rasch model, or the Rasch model with a correction for guessing, a simple model is introduced which characterizes strength of response in terms of the ratio of ability and difficulty parameters rather than their difference. This model provides a natural account of guessing, and has other useful things to contribute as well. It also offers an alternative to the Rasch model with the usual correction for guessing. The three models are compared in terms of statistical properties and fits to actual data. The goal of the paper is to widen the range of “minimal” models available to test analysts.

Liechty, Pieters & Wedel (2003) developed a hidden Markov Model (HMM) to identify the states of an attentional process in an advertisement viewing task. This work is significant because it demonstrates the benefits of stochastic modeling and Bayesian estimation in making inferences about cognitive processes based on eye movement data. One limitation of the proposed approach is that attention is conceptualized as an autonomous random process that is affected neither by the overall layout of the stimulus nor by the visual information perceived during the current fixation. An alternative model based on the input-output hidden Markov model (IOHMM; Bengio, 1999) is suggested as an extension of the HMM. The need for further studies that validate the HMM classification results is also discussed.

Multiple regression is frequently used across the various social sciences to analyze cross-sectional data. However, it can often times be challenging to justify the assumption of common regression coefficients across all respondents. This manuscript presents a heterogeneous Bayesian regression model that enables the estimation of individual-level-regression coefficients in cross-sectional data involving a single observation per response unit. A Gibbs sampling algorithm is developed to implement the proposed Bayesian methodology. A Monte Carlo simulation study is constructed to assess the performance of the proposed methodology across a number of experimental factors. We then apply the proposed method to analyze data collected from a consumer psychology study that examines the differential importance of price and quality in determining perceived value evaluations.

The present paper introduces a new explanatory item response model to account for the learning that takes place during a psychometric test due to the repeated use of the operations involved in the items. The proposed model is an extension of the operation-specific learning model (Fischer and Formann in Appl Psychol Meas 6:397–416, 1982; Scheiblechner in Z für Exp Angew Psychol 19:476–506, 1972; Spada in Spada and Kempf (eds.) Structural models of thinking and learning, Huber, Bern, Germany, pp 227–262, 1977). The paper discusses special cases of the model, which, together with the general formulation, differ in the type of response in which the model states that learning occurs: (1) correct and incorrect responses equally (non-contingent learning); (2) correct responses only (contingent learning); and (3) correct and incorrect responses to a different extent (differential contingent learning). A Bayesian framework is adopted for model estimation and evaluation. A simulation study is conducted to examine the performance of the estimation and evaluation methods in recovering the true parameters and selecting the true model. Finally, an empirical study is presented to illustrate the applicability of the model to detect learning effects using real data.

Making inferences from IRT-based test scores requires accurate and reliable methods of person parameter estimation. Given an already calibrated set of item parameters, the latent trait could be estimated either via maximum likelihood estimation (MLE) or using Bayesian methods such as maximum a posteriori (MAP) estimation or expected a posteriori (EAP) estimation. In addition, Warm’s (Psychometrika 54:427–450, 1989) weighted likelihood estimation method was proposed to reduce the bias of the latent trait estimate in unidimensional models. In this paper, we extend the weighted MLE method to multidimensional models. This new method, denoted as multivariate weighted MLE (MWLE), is proposed to reduce the bias of the MLE even for short tests. MWLE is compared to alternative estimators (i.e., MLE, MAP and EAP) and shown, both analytically and through simulations studies, to be more accurate in terms of bias than MLE while maintaining a similar variance. In contrast, Bayesian estimators (i.e., MAP and EAP) result in biased estimates with smaller variability.

In the psycholinguistic literature, reaction times and accuracy can be analyzed separately using mixed (logistic) effects models with crossed random effects for item and subject. Given the potential correlation between these two outcomes, a joint model for the reaction time and accuracy may provide further insight. In this paper, a Bayesian hierarchical framework is proposed that allows estimation of the correlation between time intensity and difficulty at the item level, and between speed and ability at the subject level. The framework is shown to be flexible in that reaction times can follow a (log-) normal or (shifted) Weibull distribution. A simulation study reveals the reduction in bias gains possible when using joint models, and an analysis of an example from a Dutch–English word recognition study illustrates the proposed method.

Estimating the ideological positions of political actors is an important step toward answering a number of substantive questions in political science. Survey scales provide useful data for such estimation, but also present a challenge, as respondents tend to interpret the scales differently. The Aldrich–McKelvey model addresses this challenge, but the existing implementations of the model still have notable shortcomings. Focusing on the Bayesian version of the model (BAM), the analyses in this article demonstrate that the model is prone to overfitting and yields poor results for a considerable share of respondents. The article addresses these shortcomings by developing a hierarchical Bayesian version of the model (HBAM). The new version treats self-placements as data to be included in the likelihood function while also modifying the likelihood to allow for scale flipping. The resulting model outperforms the existing Bayesian version both on real data and in a Monte Carlo study. An R package implementing the models in Stan is provided to facilitate future use.

Dynamic Network Actor Models (DyNAMs) assume that an observed sequence of relational events is the outcome of an actor-oriented decision process consisting of two decision levels. The first level represents the time until an actor initiates the next relational event, modeled by an exponential distribution with an actor-specific activity rate. The second level describes the choice of the receiver of the event, modeled by a conditional multinomial logit model. The DyNAM assumes that the parameters are constant over the actors and the context. This homogeneity assumption, albeit statistically and computationally convenient, is difficult to justify, e.g., in the presence of unobserved differences between actors or contexts. In this paper, we extend DyNAMs by including random-effects parameters that vary across actors or contexts and allow controlling for unknown sources of heterogeneity. We illustrate the model by analyzing relational events among the users of an online community of aspiring and professional digital and graphic designers.

Ensuring descriptive representation of racial minorities without packing minorities too heavily into districts is a perpetual difficulty, especially in states lacking voter file race data. One advance since the 2010 redistricting cycle is the advent of Bayesian Improved Surname Geocoding (BISG), which greatly improves upon previous ecological inference methods in identifying voter race. In this article, we test the viability of employing BISG to redistricting under two posterior allocation methods for race assignment: plurality versus probabilistic. We validate these methods through 10,000 redistricting simulations of North Carolina and Georgia’s congressional districts and compare BISG estimates to actual voter file racial data. We find that probabilistic summing of the BISG posteriors significantly reduces error rates at the precinct and district level relative to plurality racial assignment, and therefore should be the preferred method when using BISG for redistricting. Our results suggest that BISG can aid in the construction of majority-minority districts during the redistricting process.

This paper derives a new set of results that provide corrective measures of overall technical inefficiency that either have been ignored or wrongly assumed in the literature. Using directional distance functions, we argue that overall technical inefficiency is not only a function of input and output technical inefficiencies as previous studies claim but also of the interaction between them. The derivation of the interactive effects between input and output technical inefficiencies (IEIOs) solves the arbitrary decomposition of overall technical inefficiency into input and output components. We also show that the IEIO depends on the choice of the directional vector and whether quantities and prices are taken into consideration. Using exogenous and endogenous directional vectors, we prove these results theoretically and empirically using the US commercial banking data set. Using Bayesian estimation with the monotonicity conditions imposed at each observation, we estimate input and output technical inefficiencies separately using directional input and output distance functions with the three commonly used directional vectors; the unit value, the observed input−output, and the optimal directional vectors. The overall technical inefficiency is estimated using systems of equations to incorporate the interactive effect equation and to address the endogeneity of inputs and outputs. Consistent with the theoretical results, we find significant evidence of the IEIO which has a negative effect on the overall technical inefficiency. This result is robust to alternative directional vectors and model specifications, suggesting that the adjustability of both inputs and outputs is required for the improvement of the efficiency of the US commercial banks.

The purpose of this paper is to focus directly on the phase shift. For one thing, we ask whether a New Keynesian sticky-price model economy can account for both countercyclical prices and procyclical inflation. We present findings in which the price level is countercyclical and the inflation rate is procyclical. We proceed to use the model economy as an identification mechanism. What set of individual shocks are necessary to account for the phase shift? That set contains the price markup shock. Next, we ask what set of shocks are sufficient to account for the phase shift. This set contains three elements: the price markup and wage markup shocks along with the government spending shock. The results are important as a building block. We infer that price stickiness is an important model feature; without price stickiness, we are in the real business cycle economies that Cooley and Hansen studied. But, it raises further questions. For instance, is price stickiness of the Calvo form—the one used here—necessary to explain the phase shift?

Information about the ideological positions of different political actors is crucial in answering questions regarding political representation, polarization, and voting behavior. One way to obtain such information is to ask survey respondents to place actors on a common ideological scale, but, unfortunately, respondents typically display a set of biases when performing such placements. Key among these are rationalization bias and differential item functioning (DIF). While Aldrich–McKelvey (AM) scaling offers a useful solution to DIF, it ignores the issue of rationalization bias, and this study presents Monte Carlo simulations demonstrating that AM-type models thus can give inaccurate results. As a response to this challenge, this study develops an alternative Bayesian scaling approach, which simultaneously estimates DIF and rationalization bias, and therefore performs better when the latter bias is present.

Experiments should be designed to facilitate the detection of experimental measurement error. To this end, we advocate the implementation of identical experimental protocols employing diverse experimental modes. We suggest iterative nonparametric estimation techniques for assessing the magnitude of heterogeneous treatment effects across these modes. And we propose two diagnostic strategies—measurement metrics embedded in experiments, and measurement experiments—that help assess whether any observed heterogeneity reflects experimental measurement error. To illustrate our argument, first we conduct and analyze results from four identical interactive experiments: in the lab; online with subjects from the CESS lab subject pool; online with an online subject pool; and online with MTurk workers. Second, we implement a measurement experiment in India with CESS Online subjects and MTurk workers.