OBJECTIVE: This study aimed to examine if the General Health Questionnaire (GHQ)-12 and Kessler 6 (K6) assess the same underlying construct and to develop a score conversion table for the two scales.
METHODS: A random sample of 4303 people who completed both the GHQ-12 and K6 in 2021 were analyzed. Exploratory bifactor analysis evaluated if both scales measured the same construct, and Rasch analysis assessed item severities. The scales were transformed using Equipercentile equivalence for comparability and score conversion. Agreement was estimated with Cohen\'s Kappa coefficient, along with raw positive and negative agreement.
RESULTS: We found that the two scales measure the same phenomenon to the extent that they can be made equivalent. Conversion tables between GHQ-12 and K6 are presented. Applying the commonly used cut-off of ≥3 on the GHQ-12 bi-modal scoring, we found that the best corresponding cut-off on the K6 would be ≥8. The prevalence of psychological distress was then 22% with GHQ-12% and 21% with K6.
CONCLUSIONS: The GHQ-12 and K6 measure the same construct and corresponding cut-off scores on one scale were found for the other scale. This is valuable for longitudinal studies or time series where one scale has replaced the other scale.

BACKGROUND: The Patient Health Questionnaire (PHQ-9) and Montgomery-Asberg Depression Rating Scale (MADRS) are commonly used scales to measure depression severity in older adults.
METHODS: We utilized data from the Optimizing Outcomes of Treatment-Resistant Depression in Older Adults (OPTIMUM) clinical trial to produce conversion tables relating PHQ-9 and MADRS total scores. We split the sample into training (N = 555) and validation samples (N = 187). Equipercentile linking was performed on the training sample to produce conversion tables for PHQ-9 and MADRS. We compared the original and estimated scores in the validation sample with Bland-Altman analysis. We compared the depression severity level using the original and estimated scores with Chi-square tests.
RESULTS: The Bland-Altman analysis confirmed that differences between the original and estimated scores for at least 95 % of the sample fit within 1.96 standard deviations of the mean difference. Chi-square tests showed a significant difference in the proportion of participants at each depression severity category determined using the original and estimated scores.
CONCLUSIONS: The conversion tables should be used with caution when comparing depression severity at the individual level.
CONCLUSIONS: Our conversion tables relating PHQ-9 and MADRS scores can be used to compare treatment outcomes using aggregate data in studies that only used one of these scales.

Equating is a statistical procedure used to adjust for the difference in form difficulty such that scores on those forms can be used and interpreted comparably. In practice, however, equating methods are often implemented without considering the extent to which two forms differ in difficulty. The study aims to examine the effect of the magnitude of a form difficulty difference on equating results under random group (RG) and common-item nonequivalent group (CINEG) designs. Specifically, this study evaluates the performance of six equating methods under a set of simulation conditions including varying levels of form difference. Results revealed that, under the RG design, mean equating was proven to be the most accurate method when there is no or small form difference, whereas equipercentile is the most accurate method when the difficulty difference is medium or large. Under the CINEG design, Tucker Linear was found to be the most accurate method when the difficulty difference is medium or small, and either chained equipercentile or frequency estimation is preferred with a large difficulty level. This study would provide practitioners with research evidence-based guidance in the choice of equating methods with varying levels of form difference. As the condition of no form difficulty difference is also included, this study would inform testing companies of appropriate equating methods when two forms are similar in difficulty level.

OBJECTIVE: To develop a simple, practical methodology to equate or link equivalent domains of the 36-item Short-Form Health Survey (SF-36) and the Patient-Reported Outcomes Measurement Information System 29-item questionnaire (PROMIS-29) using the Rasch framework.
METHODS: In April 2016, the PROMIS-29 and SF-36 were completed by 1501 individuals selected to be representative of the French population. For each domain common to the two questionnaires, a Partial Credit Model was fitted to the items related to that dimension in the two questionnaires. These items were then calibrated on the same metric, which enabled the scores from one questionnaire to be associated with the scores from the other.
RESULTS: Six of the seven PROMIS-29 scales and five of the six SF-36 subscales (physical, pain, social, vitality, depression and anxiety domains) were equated or linked. Correspondence tables between scores, with a 95% confidence interval, were established for each domain. A freely available Stata macro program was developed to automatize the equating or linking process.
CONCLUSIONS: These results should facilitate comparisons across studies using the SF-36 and the PROMIS-29 in France. The equating or linking process developed is simple to implement and can be used in other countries and for other instruments.

Words read correctly per minute (WCPM) is the reporting score metric in oral reading fluency (ORF) assessments, which is popularly utilized as part of curriculum-based measurements to screen at-risk readers and to monitor progress of students who receive interventions. Just like other types of assessments with multiple forms, equating would be necessary when WCPM scores are obtained from multiple ORF passages to be compared both between and within students. This article proposes a model-based approach for equating WCPM scores. A simulation study was conducted to evaluate the performance of the model-based equating approach along with some observed-score equating methods with external anchor test design.

This simulation study investigated to what extent departures from construct similarity as well as differences in the difficulty and targeting of scales impact the score transformation when scales are equated by means of concurrent calibration using the partial credit model with a common person design. Practical implications of the simulation results are discussed with a focus on scale equating in health-related research settings. The study simulated data for two scales, varying the number of items and the sample sizes. The factor correlation between scales was used to operationalize construct similarity. Targeting of the scales was operationalized through increasing departure from equal difficulty and by varying the dispersion of the item and person parameters in each scale. The results show that low similarity between scales goes along with lower transformation precision. In cases with equal levels of similarity, precision improves in settings where the range of the item parameters is encompassing the person parameters range. With decreasing similarity, score transformation precision benefits more from good targeting. Difficulty shifts up to two logits somewhat increased the estimation bias but without affecting the transformation precision. The observed robustness against difficulty shifts supports the advantage of applying a true-score equating methods over identity equating, which was used as a naive baseline method for comparison. Finally, larger sample size did not improve the transformation precision in this study, longer scales improved only marginally the quality of the equating. The insights from the simulation study are used in a real-data example.

The part of responses that is absent in the nonequivalent groups with anchor test (NEAT) design can be managed to a planned missing scenario. In the context of small sample sizes, we present a machine learning (ML)-based imputation technique called chaining random forests (CRF) to perform equating tasks within the NEAT design. Specifically, seven CRF-based imputation equating methods are proposed based on different data augmentation methods. The equating performance of the proposed methods is examined through a simulation study. Five factors are considered: (a) test length (20, 30, 40, 50), (b) sample size per test form (50 versus 100), (c) ratio of common/anchor items (0.2 versus 0.3), and (d) equivalent versus nonequivalent groups taking the two forms (no mean difference versus a mean difference of 0.5), and (e) three different types of anchors (random, easy, and hard), resulting in 96 conditions. In addition, five traditional equating methods, (1) Tucker method; (2) Levine observed score method; (3) equipercentile equating method; (4) circle-arc method; and (5) concurrent calibration based on Rasch model, were also considered, plus seven CRF-based imputation equating methods for a total of 12 methods in this study. The findings suggest that benefiting from the advantages of ML techniques, CRF-based methods that incorporate the equating result of the Tucker method, such as IMP_total_Tucker, IMP_pair_Tucker, and IMP_Tucker_cirlce methods, can yield more robust and trustable estimates for the \"missingness\" in an equating task and therefore result in more accurate equated scores than other counterparts in short-length tests with small samples.

BACKGROUND: The present study aimed at deriving equating norms to estimate scores on the Edinburgh Cognitive and Behavioural ALS Screen (ECAS) based on those on the ALS Cognitive Behavioral Screen (ALS-CBS™) in an Italian cohort of non-demented ALS patients.
METHODS: ALS-CBS™ and ECAS scores of 293 ALS patients without frontotemporal dementia were retrospectively retrieved. Concurrent validity of the ALS-CBS™ towards the ECAS was tested by covarying for demographics, disease duration and severity, presence of C9orf72 hexanucleotide repeat expansion and behavioural features. A linear-smoothing equipercentile equating (LSEE) model was employed to derive ALS-CBS™-to-ECAS cross-walks. Gaps in LSEE-based estimation were managed via a linear regression-based equating approach. Equivalence between empirical and derived ECAS scores was tested via a two-one-sided test (TOST) procedure for the dependent sample.
RESULTS: The ALS-CBS™ predicted the ECAS (β = 0.75), accounting for the vast majority of its variance (60% out of an R2 = 0.71). Consistently, a strong, one-to-one linear association between ALS-CBS™ and ECAS scores was detected (r = 0.84; R2 = 0.73). The LSEE was able to estimate conversions for the full range of the ALS-CBS™, except for raw scores equal to 1 and 6 - for whom a linear equating-based equation was derived. Empirical ECAS scores were equivalent to those derived with both methods.
CONCLUSIONS: Italian practitioners and researchers have been herewith provided with valid, straightforward cross-walks to estimate the ECAS based on ALS-CBS™ scores in non-demented ALS patients. Conversions herewith provided will help avoid cross-sectional/longitudinal inconsistencies in test adoption within research, and possibly clinical, settings.

Test equating is a statistical procedure to ensure that scores from different test forms can be used interchangeably. There are several methodologies available to perform equating, some of which are based on the Classical Test Theory (CTT) framework and others are based on the Item Response Theory (IRT) framework. This article compares equating transformations originated from three different frameworks, namely IRT Observed-Score Equating (IRTOSE), Kernel Equating (KE), and IRT Kernel Equating (IRTKE). The comparisons were made under different data-generating scenarios, which include the development of a novel data-generation procedure that allows the simulation of test data without relying on IRT parameters while still providing control over some test score properties such as distribution skewness and item difficulty. Our results suggest that IRT methods tend to provide better results than KE even when the data are not generated from IRT processes. KE might be able to provide satisfactory results if a proper pre-smoothing solution can be found, while also being much faster than IRT methods. For daily applications, we recommend observing the sensibility of the results to the equating method, minding the importance of good model fit and meeting the assumptions of the framework.

Early and accurate detection of cognitive changes using simple tools is essential for an appropriate referral to a more detailed neurocognitive assessment and for the implementation of therapeutic strategies. The Mini-Mental Status Examination (MMSE) and the Montreal Cognitive Assessment (MoCA) are two commonly used psychometric tests for cognitive screening. Both tests have different strengths and weaknesses. Preferences regarding test selection may therefore differ among clinicians. The aim of this retrospective observational cohort study was to define corresponding scores for the MMSE and the MoCA.
We examined the relationship between the cognitive screening tests in 803 German-speaking Memory Clinic outpatients, encompassing a wide range of neurocognitive disorders. We produced a conversion table using the equipercentile equating method with log-linear smoothing. In addition, we conducted a systematic review of existing MMSE-MoCA conversions to create a table allowing for the conversion of MoCA scores into MMSE scores and vice versa using the weighted mean method.
The Memory Clinic sample showed that the prediction of MMSE to MoCA was overall less accurate compared to the conversion from MoCA to MMSE. The 19 studies included after thorough literature search showed that MoCA scores were consistently lower than MMSE scores. Eleven of 19 conversion studies had addressed the conversion of the MoCA to the MMSE, while two studies converted MMSE to MoCA scores. Another six studies applied bi-directional conversions. We provide an easy-to-use table covering the entire range of scores and taking into account all currently existing conversion formulas.
The comprehensive MMSE-MoCA conversion table enables a direct comparison of cognitive test scores at screening examinations and over the course of disease in patients with neurocognitive disorders.