A semiparametric approach for item response function estimation to detect item misfit

When scaling data using item response theory, valid statements based on the measurement model are only permissible if the model fits the data. Most item fit statistics used to assess the fit between observed item responses and the item responses predicted by the measurement model show significant weaknesses, such as the dependence of fit statistics on sample size and number of items. In order to assess the size of misfit and to thus use the fit statistic as an effect size, dependencies on properties of the data set are undesirable. The present study describes a new approach and empirically tests it for consistency. We developed an estimator of the distance between the predicted item response functions (IRFs) and the true IRFs by semiparametric adaptation of IRFs. For the semiparametric adaptation, the approach of extended basis functions due to Ramsay and Silverman (2005) is used. The IRF is defined as the sum of a linear term and a more flexible term constructed via basis function expansions. The group lasso method is applied as a regularization of the flexible term, and determines whether all parameters of the basis functions are fixed at zero or freely estimated. Thus, the method serves as a selection criterion for items that should be adjusted semiparametrically. The distance between the predicted and semiparametrically adjusted IRF of misfitting items can then be determined by describing the fitting items by the parametric form of the IRF and the misfitting items by the semiparametric approach. In a simulation study, we demonstrated that the proposed method delivers satisfactory results in large samples (i.e., N ≥ 1,000).     

Adaptive reasoning: Componential and eye movement analysis of geometric analogy performance

The present study explored individual differences in performance of a geometric analogies task. Whereas past studies employed true/false or two-alternative items, the present research included four-alternative items and studied eye movements and confidence judgements for each item performance as well as latency and error. Item difficulty proved to be a function of an interaction between the number of response alternatives and the number of elements in items, especially for subjects lower in fluid-analytic reasoning ability. Results were interpreted using two hypothesized performance strategies: constructive matching and response elimination. The less efficient of these, response elimination, seemed to be used more by lower ability subjects on more difficult items. While two previous theories resemble one or the other of these strategies, neither alone seems to capture the complexity of adaptive problem solving. It appears that a comprehensive theory should incorporate strategy shifting as a function of item difficulty and subject ability.Componential models, based in part on past research, revealed that a justification component was activated and deactivated depending upon the nature of the analogy being solved. In addition, two new components, spatial inference and spatial application, were identified as important on some items, suggesting that different geometric analogy items invoke different cognitive processing components. Thus, a comprehensive theory should also describe component activation and deactivation.     

The unique correspondence of the item response function and item category response functions in polytomously scored item response models

The item response function (IRF) for a polytomously scored item is defined as a weighted sum of the item category response functions (ICRF, the probability of getting a particular score for a randomly sampled examinee of ability ). This paper establishes the correspondence between an IRF and a unique set of ICRFs for two of the most commonly used polytomous IRT models (the partial credit models and the graded response model). Specifically, a proof of the following assertion is provided for these models: If two items have the same IRF, then they must have the same number of categories; moreover, they must consist of the same ICRFs. As a corollary, for the Rasch dichotomous model, if two tests have the same test characteristic function (TCF), then they must have the same number of items. Moreover, for each item in one of the tests, an item in the other test with an identical IRF must exist. Theoretical as well as practical implications of these results are discussed.This research was supported by Educational Testing Service Allocation Projects No. 79409 and No. 79413. The authors wish to thank John Donoghue, Ming-Mei Wang, Rebecca Zwick, and Zhiliang Ying for their useful comments and discussions. The authors also wish to thank three anonymous reviewers for their comments.     

Local context effects during emotional item directed forgetting in younger and older adults

This paper explored the differential sensitivity young and older adults exhibit to the local context of items entering memory. We examined trial-to-trial performance during an item directed forgetting task for positive, negative, and neutral (or baseline) words each cued as either to-be-remembered (TBR) or to-be-forgotten (TBF). This allowed us to focus on how variations in emotional valence (independent of arousal) and instruction (TBR vs. TBF) of the previous item (trial n-1) impacted memory for the current item (trial n) during encoding. Different from research showing impairing effects of emotional arousal, both age groups showed a memorial boost for stimuli when preceded by items high in positive or negative valence relative to those preceded by neutral items. This advantage was particularly prominent for neutral trial n items that followed emotional items suggesting that, regardless of age, neutral memories may be strengthened by a local context that is high in valence. A trending age difference also emerged with older adults showing greater sensitivity when encoding instructions changed between trial n-1 and n. Results are discussed in light of age-related theories of cognitive and emotional processing, highlighting the need to consider the dynamic, moment-to-moment fluctuations of these systems.     

A nonparametric item analysis of a selected item subset of the Learning Process Questionnaire

Background: Although there have been numerous studies conducted on the psychometric properties of Biggs' Learning Process Questionnaire (LPQ), these have involved the use of traditional omnibus measures of scale quality such as corrected item total correlations, internal consistency estimates of reliability, and factor analysis. However, these omnibus measures of scale quality are sample dependent and fail to model item responses as a function of trait level. And since the item trait relationship is typically nonlinear, traditional factor analytic methods are inappropriate. Aims: The purpose of this study was to identify a unidimensional subset of LPQ items and examine the effectiveness of these items and their options in discriminating between changes in the underlying trait level. In addition to assessing item quality, we were interested in assessing overall scale quality with non‐sample dependent measures. Method: The sample was split into two nearly equal halves, and a undimensional subset of items was identified in one of these samples and cross‐validated in the other. The nonlinear relationship between the probability of endorsing an item option and the underlying trait level was modelled using a nonparametric latent trait technique known as kernel smoothing and implemented with the program TestGraf. After item and scale quality were established, maximum likelihood estimates of participants' trait level were obtained and used to examine grade and gender differences. Results: A undimensional subset of 16 deep and achieving items was identified. Slightly more than half of these items needed some of their options combined so that the probability of endorsing an item option as a function of increasing trait level corresponded to the ideal rank ordering of the item options. With this adjustment, scale quality as measured by the information function and standard error function was found to be good. However, no statistically significant gender differences were observed and, although statistically significant grade differences were observed, they were not substantively meaningful. Conclusions: The use of nonparametric kernel‐smoothing techniques is advocated over parametric latent trait methods for the analysis of attitudinal and psychological measures involving polychotomous ordered‐response categories. It is also suggested that latent trait methods are more appropriate than traditional test‐based measures for studying differential item functioning both within and between cultures. Nonparametric kernel‐smoothing techniques hold particular promise in identifying and understanding cross‐cultural differences in student approaches to learning at both the item and scale level.     

Latent class models for testing monotonicity and invariant item ordering for polytomous items

Two assumptions that are relevant to many applications using item response theory are the assumptions of monotonicity (M) and invariant item ordering (IIO). A latent class model is proposed for ordinal items with inequality constraints on the class-specific item means. This model is used as a tool for testing for violations of M and IIO. A Gibbs sampling scheme is used for estimating the model parameters. It is shown that the deviance information criterion can be used as an overall test of M and IIO, while posterior predictive checks can be used to test these assumptions at the item level. A real data application illustrates a model-fitting strategy for detecting items that violate M and IIO.     

Effects of item difficulty on the retrieval of solutions during cognitive skill acquisition: age differences

In cognitive skill learning, shifts to better strategies for obtaining solutions often occur while associations between problems and solutions are being strengthened. In two skill learning experiments, we examined the effects of item difficulty on the retrieval of solutions and the learning of problem-solution associations in younger and older adults. The results of both experiments demonstrated an 'easy effect' in both younger and older adults, such that the retrieval of solutions as well recognition memory for problems was best for the easier items. In addition, a 'hard effect' was found in younger adults, but not in older adults, whereby the retrieval of solutions as well as recognition memory for problems was better for harder items than for medium-difficulty items. The finding that increased computational demands at the item level delayed item memorization and the retrieval of solutions in older adults but not younger adults is consistent with a general-resources account of age-related differences in skill learning.     

让自适应测验更知人善选——基于推荐系统的选题策略

基于推荐系统中协同过滤推荐的思想, 提出两种可以利用已有答题者数据的CAT选题策略：直接基于答题者推荐(DEBR)和间接基于答题者推荐(IEBR)。通过两个模拟研究, 在不同题库和不同长度的测验中, 比较了两种推荐选题策略与两种传统选题策略(FMI和BAS)在测量精度和对题目曝光率控制上的表现, 以及影响推荐选题策略表现的因素。结果发现：两种推荐选题策略对题目曝光率的控制优于两种传统选题策略, 测量精度不亚于BAS方法, 其中DEBR侧重选题精度, IEBR对题目曝光率控制最好。已有答题者数据的特点和质量是影响推荐选题策略表现的主要因素。     

The use of item scores and response times to detect examinees who may have benefited from item preknowledge

According to Wollack and Schoenig (2018, The Sage encyclopedia of educational research, measurement, and evaluation. Thousand Oaks, CA: Sage, 260), benefiting from item preknowledge is one of the three broad types of test fraud that occur in educational assessments. We use tools from constrained statistical inference to suggest a new statistic that is based on item scores and response times and can be used to detect examinees who may have benefited from item preknowledge for the case when the set of compromised items is known. The asymptotic distribution of the new statistic under no preknowledge is proved to be a simple mixture of two χ² distributions. We perform a detailed simulation study to show that the Type I error rate of the new statistic is very close to the nominal level and that the power of the new statistic is satisfactory in comparison to that of the existing statistics for detecting item preknowledge based on both item scores and response times. We also include a real data example to demonstrate the usefulness of the suggested statistic.     

Predicting consistent psychological test item responses: A comparison of models

The efficacy of four models for predicting the stability of a given individual's test item responses on a structured inventory was examined. Two models were based on item characteristics alone and predicted that an individual would be most likely to change responses to items with moderate endorsement probabilities, or with moderate social desirability scale values. Two other prediction models incorporated individual differences in the perception of item characteristics by predicting that unstable items would have relatively long response latencies for an individual, or would be near an individual's threshold for responding desirably to items. Results from two studies yielded support for the following conclusions: (a) a person's test item responses are relatively stable over short time intervals; (b) items to which a person will show response changes on retest can be identified to a statistically significant degree; (c) the models based on response latencies constituted in both studies a significantly better predictor than the other models examined. The implications of these results for the threshold model were discussed as were the practical and theoretical applications of the response latency-item stability relationship at the level of an individual's test protocol.     

Item learning in cognitive skill training: Effects of item difficulty

Item difficulty effects in skill learning were examined by giving participants extensive training with repeated alphabet arithmetic problems that varied in addend size (e.g., C ? D = ? is easy; C ? J = ? is harder). Recognition memory for the items, as measured by interpolated recognition tests, was acquired early in training and was unaffected by item difficulty. Memory for the solutions to items, as measured by the participants’ strategy reports that they had retrieved, rather than computed, the solution, was acquired later and was affected by item difficulty. Solutions to easier items were learned earlier in training for both young adults (18–24 years) and older adults (60–75 years), superimposed on an overall lower level of solution learning in older participants. The results suggest that the formation of associations between problems and their solutions is effortful and shares limited processing resources with the computational demands of the problem.     

Asymptotic identifiability of nonparametric item response models

The identifiability of item response models with nonparametrically specified item characteristic curves is considered. Strict identifiability is achieved, with a fixed latent trait distribution, when only a single set of item characteristic curves can possibly generate the manifest distribution of the item responses. When item characteristic curves belong to a very general class, this property cannot be achieved. However, for assessments with many items, it is shown that all models for the manifest distribution have item characteristic curves that are very near one another and pointwise differences between them converge to zero at all values of the latent trait as the number of items increases. An upper bound for the rate at which this convergence takes place is given. The main result provides theoretical support to the practice of nonparametric item response modeling, by showing that models for long assessments have the property of asymptotic identifiability. The research was partially supported by the National Institute of Health grant R01 CA81068-01.     

Bayesian item fit analysis for unidimensional item response theory models

Assessing item fit for unidimensional item response theory models for dichotomous items has always been an issue of enormous interest, but there exists no unanimously agreed item fit diagnostic for these models, and hence there is room for further investigation of the area. This paper employs the posterior predictive model‐checking method, a popular Bayesian model‐checking tool, to examine item fit for the above‐mentioned models. An item fit plot, comparing the observed and predicted proportion‐correct scores of examinees with different raw scores, is suggested. This paper also suggests how to obtain posterior predictive p‐values (which are natural Bayesian p‐values) for the item fit statistics of Orlando and Thissen that summarize numerically the information in the above‐mentioned item fit plots. A number of simulation studies and a real data application demonstrate the effectiveness of the suggested item fit diagnostics. The suggested techniques seem to have adequate power and reasonable Type I error rate, and psychometricians will find them promising.     

On Minimizing Guessing Effects on Multiple‐Choice Items: Superiority of a two solutions and three distractors item format to a one solution and five distractors item format

Multiple‐choice response formats are troublesome, as an item is often scored as solved simply because the examinee may be lucky at guessing the correct option. Instead of pertinent Item Response Theory models, which take guessing effects into account, this paper considers a psycho‐technological approach to re‐conceptualizing multiple‐choice response formats. The free‐response format is compared with two different multiple‐choice formats: a traditional format with a single correct response option and five distractors (‘1 of 6’), and another with five response options, three of them being distractors and two of them being correct (‘2 of 5’). For the latter format, an item is scored as mastered only if both correct response options and none of the distractors are marked. After the exclusion of a few items, the Rasch model analyses revealed appropriate fit for 188 items altogether. The resulting item‐difficulty parameters were used for comparison. The multiple‐choice format ‘1 of 6’ differs significantly from the multiple‐choice format ‘2 of 5’, while the latter does not differ significantly from the free‐response format. The lower difficulty of items ‘1 of 6’ suggests guessing effects.     

Computerized adaptive personality assessment: an illustration with the Absorption scale

This article introduces the theory behind and applications of adaptive personality assessment based on the item response theory. Two adaptive testing strategies were compared: (a) fixed test length and (b) clinical decision. Real-data simulations, based on the item responses from 1,000 subjects who had previously taken the 34-item Absorption scale (Tellegen, 1982) by means of paper-and-pencil format, were used to illustrate these strategies. Results suggest that computerized adaptive personality assessment works impressively well. With the fixed-test-length strategy, a 50% savings in administered items was achieved with little loss of measurement precision. In the clinical-decision testing strategy, individuals who were extreme on the Absorption trait were identified with perfect accuracy using, on average, 25% of the available items. The implications of these results for personality research and assessment are discussed.     

Parallel interactive retrieval of item and associative information from event memory

Memory contains information about individual events (items) and combinations of events (associations). Despite the fundamental importance of this distinction, it remains unclear exactly how these two kinds of information are stored and whether different processes are used to retrieve them. We use both model-independent qualitative properties of response dynamics and quantitative modeling of individuals to address these issues. Item and associative information are not independent and they are retrieved concurrently via interacting processes. During retrieval, matching item and associative information mutually facilitate one another to yield an amplified holistic signal. Modeling of individuals suggests that this kind of facilitation between item and associative retrieval is a ubiquitous feature of human memory.     

Conjunctive item response theory kernels

Conjunctive item response models are introduced such that (a) sufficient statistics for latent traits are not necessarily additive in item scores; (b) items are not necessarily locally independent; and (c) existing compensatory (additive) item response models including the binomial, Rasch, logistic, and general locally independent model are special cases. Simple estimates and hypothesis tests for conjunctive models are introduced and evaluated as well. Conjunctive models are also identified with cognitive models that assume the existence of several individually necessary component processes for a global ability. It is concluded that conjunctive models and methods may show promise for constructing improved tests and uncovering conjunctive cognitive structure. It is also concluded that conjunctive item response theory may help to clarify the relationships between local dependence, multidimensionality, and item response function form.I appreciate the many helpful suggestions that were given by the reviewers and Ivo Molenaar.     

Scale validation via quantifying item validity using the Dm index

While most validity indices are based on total test scores, this paper describes a method for quantifying the construct validity of items. The approach is based on the item selection technique originally described by Piazza in 1980. Unfortunately, Piazza's P2 index suffers from some substantial limitations. The Dm coefficient provides an alternative which can be used for item selection and provides a validity index for a set of items. The index is similar to that of traditional criterion-related validity indices. Criterion-related validity is used to demonstrate the accuracy of hypothesized relations of the measure with outcome variables of interest in research and practice. This method may be useful when the sample of items or persons is small, rendering more traditional approaches such as factor analysis or item response theory inappropriate. An example of how to use the technique is provided.     

Nonparametric polytomous IRT models for invariant item ordering, with results for parametric models

It is often considered desirable to have the same ordering of the items by difficulty across different levels of the trait or ability. Such an ordering is an invariant item ordering (IIO). An IIO facilitates the interpretation of test results. For dichotomously scored items, earlier research surveyed the theory and methods of an invariant ordering in a nonparametric IRT context. Here the focus is on polytomously scored items, and both nonparametric and parametric IRT models are considered.The absence of the IIO property in twononparametric polytomous IRT models is discussed, and two nonparametric models are discussed that imply an IIO. A method is proposed that can be used to investigate whether empirical data imply an IIO. Furthermore, only twoparametric polytomous IRT models are found to imply an IIO. These are the rating scale model (Andrich, 1978) and a restricted rating scale version of the graded response model (Muraki, 1990). Well-known models, such as the partial credit model (Masters, 1982) and the graded response model (Samejima, 1969), do no imply an IIO.