共查询到20条相似文献，搜索用时 31 毫秒
1.
Not quite normal: Consequences of violating the assumption of normality in regression mixture models
Lee Van Horn M Smith J Fagan AA Jaki T Feaster DJ Masyn K Hawkins JD Howe G 《Structural equation modeling》2012,19(2):227-249
Regression mixture models are a new approach for finding differential effects which have only recently begun to be used in applied research. This approach comes at the cost of the assumption that error terms are normally distributed within classes. The current study uses Monte Carlo simulations to explore the effects of relatively minor violations of this assumption, the use of an ordered polytomous outcome is then examined as an alternative which makes somewhat weaker assumptions, and finally both approaches are demonstrated with an applied example looking at differences in the effects of family management on the highly skewed outcome of drug use. Results show that violating the assumption of normal errors results in systematic bias in both latent class enumeration and parameter estimates. Additional classes which reflect violations of distributional assumptions are found. Under some conditions it is possible to come to conclusions that are consistent with the effects in the population, but when errors are skewed in both classes the results typically no longer reflect even the pattern of effects in the population. The polytomous regression model performs better under all scenarios examined and comes to reasonable results with the highly skewed outcome in the applied example. We recommend that careful evaluation of model sensitivity to distributional assumptions be the norm when conducting regression mixture models. 相似文献
2.
Latent class analysis often aims to relate the classes to continuous external consequences (“distal outcomes”), but estimating such relationships necessitates distributional assumptions. Lanza, Tan, and Bray (2013) suggested circumventing such assumptions with their LTB approach: Linear logistic regression of latent class membership on each distal outcome is first used, after which this estimated relationship is reversed using Bayes’ rule. However, the LTB approach currently has 3 drawbacks, which we address in this article. First, LTB interchanges the assumption of normality for one of homoskedasticity, or, equivalently, of linearity of the logistic regression, leading to bias. Fortunately, we show introducing higher order terms prevents this bias. Second, we improve coverage rates by replacing approximate standard errors with resampling methods. Finally, we introduce a bias-corrected 3-step version of LTB as a practical alternative to standard LTB. The improved LTB methods are validated by a simulation study, and an example application demonstrates their usefulness. 相似文献
3.
Taxometric procedures such as MAXEIG and factor mixture modeling (FMM) are used in latent class clustering, but they have very different sets of strengths and weaknesses. Taxometric procedures, popular in psychiatric and psychopathology applications, do not rely on distributional assumptions. Their sole purpose is to detect the presence of latent classes. The procedures capitalize on the assumption that, due to mean differences between two classes, item covariances within class are smaller than item covariances between the classes. FMM goes beyond class detection and permits the specification of hypothesis-based within-class covariance structures ranging from local independence to multidimensional within-class factor models. In principle, FMM permits the comparison of alternative models using likelihood-based indexes. These advantages come at the price of distributional assumptions. In addition, models are often highly parameterized and susceptible to misspecifications of the within-class covariance structure. Following an illustration with an empirical data set of binary depression items, the MAXEIG procedure and FMM are compared in a simulation study focusing on class detection and the assignment of subjects to the latent classes. FMM generally outperformed MAXEIG in terms of class detection and class assignment. Substantially different class sizes negatively impacted the performance of both approaches, whereas low class separation was much more problematic for MAXEIG than for the FMM. 相似文献
4.
Mark L. Berenson 《Decision Sciences Journal of Innovative Education》2013,11(3):243-262
There is consensus in the statistical literature that severe departures from its assumptions invalidate the use of regression modeling for purposes of inference. The assumptions of regression modeling are usually evaluated subjectively through visual, graphic displays in a residual analysis but such an approach, taken alone, may be insufficient for assessing the appropriateness of the fitted model. Here, an easy‐to‐use test of the assumption of equal variance (i.e., homoscedasticity) as well as model specification is provided. Given the importance of the equal‐variance assumption (i.e., if uncorrected, severe violations preclude the use of statistical inference and moderate violations result in a loss of statistical power) and given the fact that, if uncorrected, a misspecified or underspecified model could invalidate an entire study, the test developed by Halbert White in 1980 is recommended for supplementing a graphic residual analysis when teaching regression modeling to business students at both the undergraduate and graduate levels. Using this confirmatory approach to supplement a traditional residual analysis has value because students often find that graphic displays are too subjective for determining what constitutes severe from moderate departures from the equal variance assumption or for assessing patterns in plots that might indicate model misspecification or underspecification. 相似文献
5.
Bjrn Andersson 《Journal of Educational Measurement》2016,53(4):459-477
In observed‐score equipercentile equating, the goal is to make scores on two scales or tests measuring the same construct comparable by matching the percentiles of the respective score distributions. If the tests consist of different items with multiple categories for each item, a suitable model for the responses is a polytomous item response theory (IRT) model. The parameters from such a model can be utilized to derive the score probabilities for the tests and these score probabilities may then be used in observed‐score equating. In this study, the asymptotic standard errors of observed‐score equating using score probability vectors from polytomous IRT models are derived using the delta method. The results are applied to the equivalent groups design and the nonequivalent groups design with either chain equating or poststratification equating within the framework of kernel equating. The derivations are presented in a general form and specific formulas for the graded response model and the generalized partial credit model are provided. The asymptotic standard errors are accurate under several simulation conditions relating to sample size, distributional misspecification and, for the nonequivalent groups design, anchor test length. 相似文献
6.
Moritz Heene Sven Hilbert H. Harald Freudenthaler Markus Bühner 《Structural equation modeling》2013,20(1):36-50
This simulation study investigated the sensitivity of commonly used cutoff values for global-model-fit indexes, with regard to different degrees of violations of the assumption of uncorrelated errors in confirmatory factor analysis. It is shown that the global-model-fit indexes fell short in identifying weak to strong model misspecifications under both different degrees of correlated error terms, and various simulation conditions. On the basis of an example misspecification search, it is argued that global model testing must be supplemented by this procedure. Implications for the use of structural equation modeling are discussed. 相似文献
7.
《Structural equation modeling》2013,20(2):251-270
It is well known that coefficient alpha is an estimate of reliability if its underlying assumptions are met and that it is a lower-bound estimate if the assumption of essential tau equivalency is violated. Very little literature addresses the assumption of uncorrelated errors among items and the effect of violating this assumption on alpha. True score models are proposed that can account for correlated errors. These models allow random measurement errors on earlier items to affect directly or indirectly scores on later items. Coefficient alpha may yield spuriously high estimates of reliability if these true score models reflect item responding. In practice, it is important to differentiate these models from models in which the errors are correlated because 1 or more factors have been left unspecified. If the latter model is an accurate representation of item responding, the assumption of essential tau equivalency is violated and alpha is a lower-bound estimate of reliability. 相似文献
8.
Most researchers acknowledge that virtually all structural equation models (SEMs) are approximations due to violating distributional assumptions and structural misspecifications. There is a large literature on the unmet distributional assumptions, but much less on structural misspecifications. In this paper, we examine the robustness to structural misspecification of the model implied instrumental variable, two-stage least square (MIIV-2SLS) estimator of SEMs. We introduce two types of robustness: robust-unchanged and robust-consistent. We develop new robustness analytic conditions for MIIV-2SLS and illustrate these with hypothetical models, simulated data, and an empirical example. Our conditions enable a researcher to know whether, for example, a structural misspecification in the latent variable model influences the MIIV-2SLS estimator for measurement model equations and vice versa. Similarly, we establish robustness conditions for correlated errors. The new robustness conditions provide guidance on the types of structural misspecifications that affect parameter estimates and they assist in diagnosing the source of detected problems with MIIVs. 相似文献
9.
Sometimes, test‐takers may not be able to attempt all items to the best of their ability (with full effort) due to personal factors (e.g., low motivation) or testing conditions (e.g., time limit), resulting in poor performances on certain items, especially those located toward the end of a test. Standard item response theory (IRT) models fail to consider such testing behaviors. In this study, a new class of mixture IRT models was developed to account for such testing behavior in dichotomous and polytomous items, by assuming test‐takers were composed of multiple latent classes and by adding a decrement parameter to each latent class to describe performance decline. Parameter recovery, effect of model misspecification, and robustness of the linearity assumption in performance decline were evaluated using simulations. It was found that the parameters in the new models were recovered fairly well by using the freeware WinBUGS; the failure to account for such behavior by fitting standard IRT models resulted in overestimation of difficulty parameters on items located toward the end of the test and overestimation of test reliability; and the linearity assumption in performance decline was rather robust. An empirical example is provided to illustrate the applications and the implications of the new class of models. 相似文献
10.
Componential IRT models for polytomous items are of particular interest in two contexts: Componential research and test development. We assume that there are basic components, such as processes and knowledge structures, involved in solving cognitive tasks. In Componential research, the subtask paradigm may be used to isolate such components in subtasks. In test development, items may be composed such that their response alternatives correspond with specific combinations of such components. In both cases the data may be modeled as polytomous items. With Bock's (1972) nominal model as a general framework, transformation matrices can be used to constrain the parameters of the response categories so as to reflect the Componential design of the response categories. In this way, both main effects and interaction effects of components can be studied. An application to a spelling task demonstrates this approach 相似文献
11.
One of the major assumptions of item response theory (IRT)models is that performance on a set of items is unidimensional, that is, the probability of successful performance by examinees on a set of items can be modeled by a mathematical model that has only one ability parameter. In practice, this strong assumption is likely to be violated. An important pragmatic question to consider is: What are the consequences of these violations? In this research, evidence is provided of violations of unidimensionality on the verbal scale of the GRE Aptitude Test, and the impact of these violations on IRT equating is examined. Previous factor analytic research on the GRE Aptitude Test suggested that two verbal dimensions, discrete verbal (analogies, antonyms, and sentence completions)and reading comprehension, existed. Consequently, the present research involved two separate calibrations (homogeneous) of discrete verbal items and reading comprehension items as well as a single calibration (heterogeneous) of all verbal item types. Thus, each verbal item was calibrated twice and each examinee obtained three ability estimates: reading comprehension, discrete verbal, and all verbal. The comparability of ability estimates based on homogeneous calibrations (reading comprehension or discrete verbal) to each other and to the all-verbal ability estimates was examined. The effects of homogeneity of item calibration pool on estimates of item discrimination were also examined. Then the comparability of IRT equatings based on homogeneous and heterogeneous calibrations was assessed. The effects of calibration homogeneity on ability parameter estimates and discrimination parameter estimates are consistent with the existence of two highly correlated verbal dimensions. IRT equating results indicate that although violations of unidimensionality may have an impact on equating, the effect may not be substantial. 相似文献
12.
The purpose of this study is to provide guidance on a process for including latent class predictors in regression mixture models. We first examine the performance of current practice for using the 1-step and 3-step approaches where the direct covariate effect on the outcome is omitted. None of the approaches show adequate estimates of model parameters. Given that Step 1 of the 3-step approach shows adequate results in class enumeration, we suggest using an alternative approach: (a) decide the number of latent classes without predictors of latent classes, and (b) bring the latent class predictors into the model with the inclusion of hypothesized direct covariate effects. Our simulations show that this approach leads to good estimates for all model parameters. The proposed approach is demonstrated by using empirical data to examine the differential effects of family resources on students’ academic achievement outcome. Implications of the study are discussed. 相似文献
13.
Randall David Penfield 《Educational Measurement》2014,33(1):36-48
A polytomous item is one for which the responses are scored according to three or more categories. Given the increasing use of polytomous items in assessment practices, item response theory (IRT) models specialized for polytomous items are becoming increasingly common. The purpose of this ITEMS module is to provide an accessible overview of polytomous IRT models. The module presents commonly encountered polytomous IRT models, describes their properties, and contrasts their defining principles and assumptions. After completing this module, the reader should have a sound understating of what a polytomous IRT model is, the manner in which the equations of the models are generated from the model's underlying step functions, how widely used polytomous IRT models differ with respect to their definitional properties, and how to interpret the parameters of polytomous IRT models. 相似文献
14.
A latent variable modeling procedure for examining whether a studied population could be a mixture of 2 or more latent classes is discussed. The approach can be used to evaluate a single-class model vis-à-vis competing models of increasing complexity for a given set of observed variables without making any assumptions about their within-class interrelationships. The method is helpful in the initial stages of finite mixture analyses to assess whether models with 2 or more classes should be subsequently considered as opposed to a single-class model. The discussed procedure is illustrated with a numerical example. 相似文献
15.
The posterior predictive model checking method is a flexible Bayesian model‐checking tool and has recently been used to assess fit of dichotomous IRT models. This paper extended previous research to polytomous IRT models. A simulation study was conducted to explore the performance of posterior predictive model checking in evaluating different aspects of fit for unidimensional graded response models. A variety of discrepancy measures (test‐level, item‐level, and pair‐wise measures) that reflected different threats to applications of graded IRT models to performance assessments were considered. Results showed that posterior predictive model checking exhibited adequate power in detecting different aspects of misfit for graded IRT models when appropriate discrepancy measures were used. Pair‐wise measures were found more powerful in detecting violations of the unidimensionality and local independence assumptions. 相似文献
16.
Robustness of the School-Level IRT Model 总被引：1，自引：0，他引：1
Richard L. Tate 《Journal of Educational Measurement》1995,32(2):145-162
The robustness of the school-level item response theoretic (IRT) model to violations of distributional assumptions was studied in a computer simulation. Estimated precision of "expected a posteriori" (EAP) estimates of the mean school ability from BILOG 3 was compared with actual precision, varying school size, intraclass correlation, school ability, number of forms comprising the test, and item parameters. Under conditions where the school-level precision might be possibly acceptable for real school comparisons, the EAP estimates of school ability were robust over a wide range of violations and conditions, with the estimated precision being either consistent with the actual precision or somewhat conservative. Some lack of robustness was found, however, under conditions where the precision was inherently poor and the test would presumably not be used for serious school comparisons. 相似文献
17.
In this article we describe a structural equation modeling (SEM) framework that allows nonnormal skewed distributions for the continuous observed and latent variables. This framework is based on the multivariate restricted skew t distribution. We demonstrate the advantages of skewed SEM over standard SEM modeling and challenge the notion that structural equation models should be based only on sample means and covariances. The skewed continuous distributions are also very useful in finite mixture modeling as they prevent the formation of spurious classes formed purely to compensate for deviations in the distributions from the standard bell curve distribution. This framework is implemented in Mplus Version 7.2. 相似文献
18.
Michael Kane 《Journal of Educational Measurement》2002,39(2):165-181
Generalizability theory (G theory) employs random-effects ANOVA to estimate the variance components included in generalizability coefficients, standard errors, and other indices of precision. The ANOVA models depend on random sampling assumptions, and the variance-component estimates are likely to be sensitive to violations of these assumptions. Yet, generalizability studies do not typically sample randomly. This kind of inconsistency between assumptions in statistical models and actual data collection procedures is not uncommon in science, but it does raise fundamental questions about the substantive inferences based on the statistical analyses. This article reviews criticisms of sampling assumptions in G theory (and in reliability theory) and examines the feasibility of using representative sampling, stratification, homogeneity assumptions, and replications to address these criticisms. 相似文献
19.
The aim of this study is to assess the efficiency of using the multiple‐group categorical confirmatory factor analysis (MCCFA) and the robust chi‐square difference test in differential item functioning (DIF) detection for polytomous items under the minimum free baseline strategy. While testing for DIF items, despite the strong assumption that all but the examined item are set to be DIF‐free, MCCFA with such a constrained baseline approach is commonly used in the literature. The present study relaxes this strong assumption and adopts the minimum free baseline approach where, aside from those parameters constrained for identification purpose, parameters of all but the examined item are allowed to differ among groups. Based on the simulation results, the robust chi‐square difference test statistic with the mean and variance adjustment is shown to be efficient in detecting DIF for polytomous items in terms of the empirical power and Type I error rates. To sum up, MCCFA under the minimum free baseline strategy is useful for DIF detection for polytomous items. 相似文献
20.
The 3-step approach has been recently advocated over the simultaneous 1-step approach to model a distal outcome predicted by a latent categorical variable. We generalize the 3-step approach to situations where the distal outcome is predicted by multiple and possibly associated latent categorical variables. Although the simultaneous 1-step approach has been criticized, simulation studies have found that the performance of the two approaches is similar in most situations (Bakk & Vermunt, 2016). This is consistent with our findings for a 2-LV extension when all model assumptions are satisfied. Results also indicate that under various degrees of violation of the normality and conditional independence assumption for the distal outcome and indicators, both approaches are subject to bias but the 3-step approach is less sensitive. The differences in estimates using the two approaches are illustrated in an analysis of the effects of various childhood socioeconomic circumstances on body mass index at age 50. 相似文献