Sample Size Determination Within the Scope of Conditional Maximum Likelihood Estimation with Special Focus on Testing the Rasch Model

Draxler, Clemens; Alexandrowicz, Rainer W.

doi:10.1007/s11336-015-9472-y

Cited by 18 publications

(15 citation statements)

References 40 publications

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“…Additionally, in the conditional framework, a sample size around 390 participants is sufficient to detect a model deviation in item difficulty of 1 logit with a significance level of 5% and power of 80%. However, since these samples requirements are influenced by several factors including targeting [72], other authors have argued that samples with more than 250 participants provide enough power for most practical purposes [73]. The overall model fit was evaluated with a summary item-trait χ 2 statistic, which is calculated through the summation of the χ 2 of all individual items [63].…”

Section: Methodsmentioning

confidence: 99%

Stress beyond coping? A Rasch analysis of the Perceived Stress Scale (PSS-14) in an Aboriginal population

et al. 2019

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The history of colonization contributed to Aboriginal and Torres Strait Islanders becoming one of the most disadvantaged groups in Australia. The multiple social inequalities, and therefore the constant insecurities for many about low income, poor living conditions, unemployment, and discrimination, generate chronic stress in this population. In the Baby Teeth Talk Study, an oral-health randomized controlled trial, the Perceived Stress Scale (PSS-14) was administered to 367 pregnant Aboriginal women at baseline. The aim of the present study was to evaluate the validity and reliability of the PSS-14 in an Aboriginal population. The study analysed: (a) model fit; (b) dimensionality; (c) local dependence; (d) differential item functioning; (e) threshold ordering and item fit; (f) targeting; (g) reliability; and (h) criterion validity. The dimensionality analysis indicated a two-factor structure, with negatively and positively worded items clustering together and 21.7% (95% Agresti-Coull C.I. [17.8%, 26.2%]) statistically significant t-tests between the persons’ estimates. After the creation of composite items, the revised Perceived Distress (χ 2 (21) = 11.74, p = 0.946) and Perceived Coping (χ 2 (28) = 17.63, p = 0.935) subscales fitted the Rasch model. Reliability was modest (PersonSeparationIndex distress = 0.72; PersonSeparationIndex coping = 0.76). The latent correlation between the Perceived Distress and Perceived Coping subscales was r = 0.14. It is hypothesized that the social inequalities experienced by the Aboriginal population are so pronounced that even Aboriginal pregnant women that perceived themselves as coping well with life challenges ended up endorsing items regarding high levels of stress. The present research showed that a revised PSS-14 is a culturally valid and modestly reliable psychological instrument to measure stress in a population of pregnant Aboriginal women in Australia.

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Section: Methodsmentioning

confidence: 99%

Stress beyond coping? A Rasch analysis of the Perceived Stress Scale (PSS-14) in an Aboriginal population

et al. 2019

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“…Ideally, we would compare the depression across multiple cohorts, but we have extensive data on the relevant covariates for these two cohorts only and, therefore, we included only these cohorts. However, according to recent research, the sample had sufficient statistical power for estimation of RM (Draxler & Alexandrowicz, 2015). Regarding the depression items themselves, we do not have exact knowledge on the source of each individual item and how they were selected.…”

Section: Discussionmentioning

confidence: 99%

Assessment of depression in veterans across missions: a validity study using Rasch measurement models

Karstoft

Nielsen

2017

European Journal of Psychotraumatology

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Background: Depression is a common psychopathological outcome following military deployment. Previous studies have reported differing rates of post-deployment depression, indicating that the toll of war differs across missions. However, it is unclear to what degree the varying prevalence is due methodological differences. Studies comparing rates of depression across cohorts using the same methodology and ensuring measurement invariance are rare, leaving us with limited knowledge on the actual depression prevalence variance across missions. Objective: Applying Rasch models (RM), we aim to validate a measure of depression distributed to all personnel deployed with the Danish Defense since 1998. The main focus was establishing a sufficient sum score and measurement invariance relative to deployment cohort. Method: Two cohorts of the International Security Assistance Force (ISAF) deployed to Afghanistan in 2009 (ISAF7, N = 265) and 2013 (ISAF15, N = 271) were included. Participants filled out a questionnaire concerning their Psychological Reactions to International Missions (PRIM) approximately seven months after home-coming. The questionnaire included a 10-item scale of depression symptoms (PRIM-Depression). The validity of the PRIM-Depression was tested using RM with specific focus on differential item functioning (DIF) across the two cohorts. Results: The PRIM-Depression scale displayed excellent overall consistency and showed no problems with monotonicity or homogeneity. However, the full PRIM-Depression scale did not fit a pure RM. We therefore tested the fit of items to a graphical log-linear RM and found evidence of DIF for two items relative to cohort. We proceeded without these two items and tested the resulting 8-item version which fitted a pure RM without DIF on any of the exogenous variables. Conclusions: Our results suggest that the 10-item PRIM-Depression scale should be used to compare cohorts only with appropriate score equation. The 8-item version provides a sufficient statistic and can as such be applied using the raw score.

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“…For a proof of the asymptotic distribution under an alternative, we need to assume that parameters β a converge to β 0 for n → ∞. A similar method was used for CML and exponential family models (Draxler & Alexandrowicz, 2015) and for MML and tests based on contingency tables (Maydeu-Olivares & Montaño, 2013). The asymptotic distribution of the statistics depends on the consistency of the maximum likelihood (ML) parameter estimator (e.g., Casella & Berger, 2002).…”

Section: Power Analysismentioning

confidence: 99%

“…As they rely on an asymptotic result, the agreement of the corresponding expected and observed distributions will be higher in larger samples and for lower differences |β − β 0 |, i.e., lower effect sizes. The reliance on these results can be considered common practice according to Agresti (2013) and has been shown to involve only minor errors in a simulation study by Draxler and Alexandrowicz (2015) in the CML context. Also, note that the test of the null hypothesis, i.e., a test against a central χ 2 distribution, involves a similar assumption.…”

Section: Power Analysismentioning

confidence: 99%

“…As one exception, Maydeu-Olivares and Montaño (2013) have described a method of power analysis for some tests of contingency tables, such as the M 2 test. Draxler (2010) and Draxler and Alexandrowicz (2015) provided formulas to calculate the power or sample size of the Wald, LR, and score tests in the context of exponential family models and conditional maximum likelihood (CML) estimation. Two examples of exponential family models in IRT are the Rasch (Rasch, 1960) and the partial credit models (Masters, 1982), in which the parameters represent the item difficulties.…”

Section: Introductionmentioning

confidence: 99%

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Power analysis for the Wald, LR, score, and gradient tests in a marginal maximum likelihood framework: Applications in IRT

Zimmer¹,

Draxler²,

Debelak³

2021

Preprint

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The Wald, likelihood ratio, score and the recently proposed gradient statistics can be used to assess a broad range of hypotheses in item response theory models, for instance, to check the overall model fit or to detect differential item functioning. We introduce new methods for power analysis and sample size planning that can be applied when marginal maximum likelihood estimation is used. This avails the application to a variety of IRT models, which are increasingly used in practice, e.g., in large-scale educational assessments. An analytical method utilizes the asymptotic distributions of the statistics under alternative hypotheses. For a larger number of items, we also provide a sampling-based method, which is necessary due to an exponentially increasing computational load of the analytical approach. We performed extensive simulation studies in two practically relevant settings, i.e., testing a Rasch model against a 2PL model and testing for differential item functioning. The observed distributions of the test statistics and the power of the tests agreed well with the predictions by the proposed methods. We provide an openly accessible R package that implements the methods for user-supplied hypotheses.

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Sample Size Determination Within the Scope of Conditional Maximum Likelihood Estimation with Special Focus on Testing the Rasch Model

Cited by 18 publications

References 40 publications

Stress beyond coping? A Rasch analysis of the Perceived Stress Scale (PSS-14) in an Aboriginal population

Stress beyond coping? A Rasch analysis of the Perceived Stress Scale (PSS-14) in an Aboriginal population

Assessment of depression in veterans across missions: a validity study using Rasch measurement models

Power analysis for the Wald, LR, score, and gradient tests in a marginal maximum likelihood framework: Applications in IRT

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