High-dimensional Exploratory Item Factor Analysis by A Metropolis–Hastings Robbins–Monro Algorithm

Marginal maximum likelihood (MML) estimation is the preferred approach to fitting item response theory models in psychometrics due to the MML estimator's consistency, normality, and efficiency as the sample size tends to infinity. However, state-of-the-art MML estimation procedures such as the Metropolis-Hastings Robbins-Monro (MH-RM) algorithm as well as approximate MML estimation procedures such as variational inference (VI) are computationally time-consuming when the sample size and the number of latent factors are very large. In this work, we investigate a deep learning-based VI algorithm for exploratory item factor analysis (IFA) that is computationally fast even in large data sets with many latent factors. The proposed approach applies a deep artificial neural network model called an importance-weighted autoencoder (IWAE) for exploratory IFA. The IWAE approximates the MML estimator using an importance sampling technique wherein increasing the number of importance-weighted (IW) samples drawn during fitting improves the approximation, typically at the cost of decreased computational efficiency. We provide a real data application that recovers results aligning with psychological theory across random starts. Via simulation studies, we show that the IWAE yields more accurate estimates as either the sample size or the number of IW samples increases (although factor correlation and intercepts estimates exhibit some bias) and obtains similar results to MH-RM in less time. Our simulations also suggest that the proposed approach performs similarly to and is potentially faster than constrained joint maximum likelihood estimation, a fast procedure that is consistent when the sample size and the number of items simultaneously tend to infinity.

This article proposes a comprehensive approach for assessing the quality and appropriateness of exploratory factor analysis solutions intended for item calibration and individual scoring. Three groups of properties are assessed: (a) strength and replicability of the factorial solution, (b) determinacy and accuracy of the individual score estimates, and (c) closeness to unidimensionality in the case of multidimensional solutions. Within each group, indices are considered for two types of factor-analytic models: the linear model for continuous responses and the categorical-variable-methodology model that treats the item scores as ordered-categorical. All the indices proposed have been implemented in a noncommercial and widely known program for exploratory factor analysis. The usefulness of the proposal is illustrated with a real data example in the personality domain.

Identifying item–trait relationships is a core task in multidimensional item response theory (MIRT). Common empirical approaches include exploratory item factor analysis (EIFA) with rotations, the expectation maximization-based L1 regularization (EML1) algorithm, and the expectation model selection (EMS) algorithm. While these methods typically assume multivariate normality of latent traits, empirical data often deviate from this assumption. This study evaluates the robustness of EIFA, EML1, and EMS, when latent traits violate normality assumptions. Using the independent generator transform, we generate latent variables under varying levels of skewness, excess kurtosis, numbers of non-normal dimensions, and inter-factor correlations. We then assess the performance of each method in terms of the F1-score for identifying item–trait relationships and mean squared error (MSE) of parameter estimations. The results indicate that non-normality leads to a reduction in F1-score and an increase in MSE generally. For F1-score, EMS performs best with small samples (e.g., N=500), whereas EIFA with rotations yields the highest F1-score in larger samples. In terms of estimation accuracy, EMS and EML1 generally yield lower MSEs than EIFA. The effects of non-normality are also demonstrated by applying these methods to a real data set from the Depression, Anxiety, and Stress Scale.

Joint maximum likelihood (JML) estimation is one of the earliest approaches to fitting item response theory (IRT) models. This procedure treats both the item and person parameters as unknown but fixed model parameters and estimates them simultaneously by solving an optimization problem. However, the JML estimator is known to be asymptotically inconsistent for many IRT models, when the sample size goes to infinity and the number of items keeps fixed. Consequently, in the psychometrics literature, this estimator is less preferred to the marginal maximum likelihood (MML) estimator. In this paper, we re-investigate the JML estimator for high-dimensional exploratory item factor analysis, from both statistical and computational perspectives. In particular, we establish a notion of statistical consistency for a constrained JML estimator, under an asymptotic setting that both the numbers of items and people grow to infinity and that many responses may be missing. A parallel computing algorithm is proposed for this estimator that can scale to very large datasets. Via simulation studies, we show that when the dimensionality is high, the proposed estimator yields similar or even better results than those from the MML estimator, but can be obtained computationally much more efficiently. An illustrative real data example is provided based on the revised version of Eysenck's Personality Questionnaire (EPQ-R).

A healthy lifestyle is pivotal for improving mental health. As the concept of a healthy lifestyle is comprehensive, there is a need to prioritise components related to mental health in planning proper mental health interventions. In this regard, physical activity, diet, sleep quality, substance abuse and social support have been identified to enhance mental health. It is necessary to develop a valid scale for assessing healthy lifestyles related to mental health. Thus, this study aimed to adapt and validate an existing scale to evaluate healthy lifestyles related to mental health. This study included 177 (men: n=73, women: n=104) participants from University Teknologi MARA, Puncak Alam, Selangor. The data were presented using descriptive statistics and subjected to an exploratory factor analysis. The 22 scale items evaluated were valid and reliable in assessing the five components of healthy lifestyles related to mental health. The total variance explained for measuring the construct was 68.610%. The Cronbachs alpha value for the five components ranged from 0.784 to 0.903. The adapted scale is acceptable and reliable in evaluating healthy lifestyles related to mental health within the target population. Thus, it can be used to assess significant components of healthy lifestyles to promote mental health. Accordingly, relevant authorities can formulate the best strategies to enhance mental health.

在心理与教育测量中，项目反应理论（Item Response Theory，IRT）模型的参数估计方法是理论研究与实践应用的基本工具。最近，由于IRT模型的不断扩展与EM（expectation-maximization）算法自身的固有问题，参数估计方法的改进与发展显得尤为重要。这里介绍了IRT模型中边际极大似然估计的发展，提出了它的阶段性特征，即联合极大似然估计阶段、确定性潜在心理特质“填补”阶段、随机潜在心理特质“填补”阶段，重点阐述了它的潜在心理特质“填补”（dataaugmentation）思想。EM算法与Metropolis-Hastings Robbins—Monro（MH-RM）算法作为不同的潜在心理特质“填补”方法，都是边际极大似然估计的思想跨越。目前，潜在心理特质“填补”的参数估计方法仍在不断发展与完善。

Exploratory Factor analysis is one of the techniques used in the development, validation and adaptation of psychological measurement instruments. Its use spread during the 1960s and has been growing exponentially thanks to the advancement of information technology. The criteria used, of course, have also evolved. But the applied researchers, who use this technique as a routine, remain often ignorant of all this. In the last few decades numerous studies have denounced this situation. There is an urgent need to update the classic criteria. The incorporation of the most suitable criteria will improve the quality of our research. In this work we review the classic criteria and, depending on the case, we also propose current criteria to replace or complement the former. Our objective is to offer the interested applied researcher updated guidance on how to perform an Exploratory Item Factor Analysis, according to the “post-Little Jiffy” psychometrics. This review and the guide with the corresponding recommendations have been articulated in four large blocks: 1) the data type and the matrix of association, 2) the method of factor estimation, 3) the number of factors to be retained, and 4) the method of rotation and allocation of items. An abridged version of the complete guide is provided at the end of the article.

We propose a new definition of inconspicuous consumption as an individual disposition and present an instrument for measuring this variable. The article describes the successive stages of the construction of the Inconspicuous Consumption Scale (ICS). The initial set of test items was generated using the method of competent judges - qualitative and quantitative evaluation using CVR Lawshe. Next, an exploratory factor analysis was carried out using data obtained from a sample of 690 participants. In the first step, parallel analysis and the maximum average partial (MAP) criterion were conducted, while in the next step, we again performed exploratory hierarchical factor analysis using maximum likelihood ML with the promax rotation. Confirmatory structure was performed on data collected from 497 respondents (confirmatory factor analysis CFA using the robust ML estimator with the Satorra-Bentler correction).The results of a preliminary selection of items and exploratory and confirmatory factor analyses have led to the development of an instrument which measures four factors that make up the global ICS: Knowledge, Services, Experiences, and Subtle Brand Signals. Reliability and validity studies carried out in Poland in a sample of 1,330 respondents show that the ICS has satisfactory psychometric properties. We have assumed that inconspicuous consumption (IC) consists of deliberate avoidance of visibility and investments directly aimed at improving the quality of life and caring for the environment, both from a local and global perspective. Treated as an individual, relatively enduring disposition in the area of consumer behavior, it appears to be a useful construct for explainingh changes in the area of consumer behavior.

Background and Aims The estimated glomerular filtration rate (eGFR) and other kidney function markers are associated with cardiovascular disease (CVD) mortality [1]. It remains unclear whether integrating multiple kidney markers together can improve CVD mortality risk prediction and what would be an appropriate method of integration. In a small general population sample, we recently showed that confirmatory factor analysis (CFA) may predict CVD risk better than single markers, but it did not outperform cystatin C-based eGFR (eGFRcys) [2]. To assess whether our findings were context-dependent and to which extent they may extend to mortality risk assessment, we applied CFA and exploratory factor analysis (EFA), integrating five kidney function markers in the UK Biobank (UKBB) study, comparing risk discrimination for CVD mortality and renal failure mortality versus established eGFR formulas. Method We analyzed data from 366,758 UKBB participants (mean age 56.6 years; females 53.7%) without clinical history of kidney failure at baseline. Information on participants’ mortality was collected from the National Health System registry, using ICD-10 codes I00-I99 and N17-N19 to identify CVD mortality and renal failure mortality. We applied CFA and EFA to creatinine-based estimated glomerular filtration rate (eGFRcre), eGFRcys, blood urea nitrogen (BUN), uric acid (UA), and serum albumin (Alb). EFA was fitted using maximum likelihood. Promax rotation was then applied. We fitted Cox regression models to examine the associations of mortality with kidney markers: CFA-based kidney index [CFA]; 1st EFA-based kidney index [EFA1]; 2nd EFA-based kidney index [EFA2]; eGFRcre; eGFRcys; and creatinine- and cystatin C-based eGFR (eGFRcrecys). Models were adjusted for sex, age, body mass index, education, self-reported ancestry, hypertension, diabetes, and tobacco smoking. The receiver operating characteristics (ROC) curve and the DeLong test were used to compare discriminatory ability of each index. Results CFA standardized factor loadings (λ) of eGFRcre, eGFRcys, BUN, UA and Alb were 0.81, 0.73, -0.55, -0.39, and 0.12, respectively. EFA identified two factors: EFA1, largely dependent on eGFRcys (λ = 0.85), and EFA2, reflecting BUN (λ = 0.88), eGFRcre (λ = -0.55) and UA (λ = 0.36). Over a median follow-up of 12.5 years, we observed 26,327mortality cases, of which 5,376 and 45 were related to CVD and renal failure. The hazard ratios (HR) and 95% confidence intervals (CI) for CVD mortality and renal failure mortality per each standard deviation change were of 1.22 (1.19–1.25) and 3.53 (2.98–4.18) for eGFRcre, 1.62 (1.57–1.67) and 7.34 (5.82–9.27) for eGFRcys, 1.47 (1.43–1.51) and 4.82 (4.04–5.76) for eGFRcrecys, 1.38 (1.34–1.41) and 2.94 (2.63–3.29) for CFA, 1.61 (1.56–1.66) and 7.54 (5.90–9.64) for EFA1, and 1.33 (1.30–1.35) and 1.98 (1.85–2.12) for EFA2. The area under the curve (AUC) for CVD mortality risk was higher for EFA1 (0.706, 0.699–0.713) than for any other kidney marker, except for eGFRcys (0.709, 0.702–0.716). The kidney failure mortality AUC of EFA1 (0.936, 0.901–0.972) was similar to that of eGFRcys (0.939, 0.905–0.972). Conclusion To assess the contribution of kidney function to CVD-related mortality in general population studies of mainly healthy individuals, EFA is a better way than using single markers. However, EFA does not outperform eGFRcys, which, being based on a simpler calculation, remains a better choice for CVD and renal failure mortality risk prediction.

Strategic Self‐Regulation for Speaking English as a Foreign Language: Scale Development and Validation

The present study aimed at developing a valid and reliable scale for assessing attitudes towards honour killing in Pakistan. The scale was developed in three phases; item pool generation, exploratory factor analysis, and confirmatory factor analysis. The initial item pool was generated form in-depth interviews with professionals (i.e., lawyers, journalists, psychologists, religious scholars, police officials, and social activists) and perpetrators in jail. In order to validate the initial 19 item scale, 459 adults, within the age range of 18-60 years were recruited from the Federal capital city and other cities of Punjab by using convenient sampling technique. For validation of the factor structure, Exploratory Factor Analysis (EFA) was run using Maximum Likelihood (ML) extraction method and promax rotation method. The analysis yielded two factors (affirmation and deterrents of honour killing) that accounted for 32% variance. Confirmatory Factor Analysis (CFA) was carried out to validate the factor structure explored through EFA. An independent sample of 695 adults was recruited for confirmatory study. Results of CFA indicated a good model fit for the final scale comprising 17 items. The Cronbach alpha coefficients for the two factors were .79 and .61, respectively. The convergent and discriminant validity of the final scale was also determined using the Gender Role Attitude Scale (Anila & Ansari, 1992) and Extremism Scale (Gilani & Altaf, 2005.

BackgroundThe Driver Behavior Questionnaire (DBQ) is one of the most used tools for measuring self-reported aberrant driving behavior. Several versions of the DBQ exist varying in terms of the item number and factor structure.ObjectivesThis study aimed to investigate the psychometric properties and the factorial structure of the DBQ for assessing aberrant behavior among Lebanese drivers and to examine the relationship between DBQ subscales and socio-demographic characteristics and traffic-related variables.MethodsA cross-sectional study was conducted among Lebanese drivers aged over 18 years from all Lebanese governorates. Data were collected using a convenient sampling technique and an anonymous Arabic self-administered questionnaire that included socio-demographic characteristics and the Arabic Lebanese version of the DBQ (DBQ-L). Statistical analyses were performed using SPSS version 24 and Amos software. Exploratory factor analysis (N = 568) and confirmatory factor analysis (N = 534) were used to test the factorial structure of the DBQ-L. Linear regression analyses were performed to examine the association between DBQ-L, sociodemographic, and relevant traffic variables.ResultsA total of 1102 drivers aged between 18 and 82 years participated in the study with an average age of 34.64 (SD = 12.33). Of the total, 68.4% of participants were male with an average driving experience of 13.46 years (SD = 10.76). The DBQ-L total scale revealed high internal consistency (Cronbach’s α = 0.892). Exploratory and confirmatory factor analysis supported the original four-factor structure reflecting aggressive violations, ordinary violations, errors, and lapses dimensions. Aggressive violations had the highest mean among all the DBQ subscales. Men were found to have a higher tendency to commit aggressive and ordinary violations than females. Furthermore, the ordinary violation score was positively associated with younger age and increased mileage. All DBQ subscales decreased with the highest educational level. Being a professional driver increased the likelihood of drivers reporting violations, errors, and lapses, and increased mileage amplified the tendency of displaying aggressive violations and lapses when driving. However, errors decreased for young drivers and increased with age and larger driver experience.ConclusionThe cross-cultural adapted version of the DBQ was found to be a reliable and valid tool for assessing aberrant behaviors among Lebanese drivers. This study revealed distinct behavior patterns, with men frequently displaying aggressive violations, and younger, high-mileage drivers more prone to ordinary violations and lapses. Higher education correlated with safer driving, while professional drivers reported more violations, errors, and lapses. These findings highlight the importance of tailored road safety interventions based on driver demographics. Further studies are needed to examine the ability of DBQ to predict road accidents.

Aim. To define significant ultrasound and magnetic resonance imaging markers in diagnostics of the depth of chorion invasion in myometrium in pregnant women after Cesarean section was carried out.Materials and methods. 68 pregnant women from 28 to 32 gestation weeks with Caesarian scar and placenta on the front wall of uterus were retrospectively studied. Pregnant women were divided into 4 groups depending on histologic verification of placenta invasion depth. MRI and ultrasound assessment of the lower uterine segment was carried out and the most significant US and MRI markers of placenta accreta were distinguished. Subsequently, the received results of the research were processed by algorithms of factor analysis with calculation of informativeness of each marker and with determination of the forecast of placenta accreta.Results. As a result, group I of pregnant women scored within 0-0.9 conventional units, in group II – 1-3 conventional units, in group III – the score was 3.1-5.0 conventional units, in group IV – 5.1-7.0 conventional units. In groups III and IV are characterized by the fact of signs combination. In group III the combination of 2 signs was detected in 65% of cases, of 3 signs – in 25% of pregnant women.Conclusion. The most informative marker of ultrasound diagnostic of placenta accreta was determination of venous lacunas in its suprabasal part (0.42), in case of MRI it was the assessment of the bladder wall (0.45). The sensitivity and specificity of ultrasonography were 86.2% and 84.8%, in MRI they were 96% and 94.4% respectively.

It is well known that an arbitrary graphical model of statistical inference defined on a tree,i.e. on a graph without loops, is solved exactly and efficiently by an iterative beliefpropagation (BP) algorithm convergent to the unique minimum of the so-called Bethe freeenergy functional. For a general graphical model on a loopy graph, the functional may showmultiple minima, the iterative BP algorithm may converge to one of the minimaor may not converge at all, and the global minimum of the Bethe free energyfunctional is not guaranteed to correspond to the optimal maximum likelihood (ML)solution in the zero-temperature limit. However, there are exceptions to this generalrule, discussed by Kolmogorov and Wainwright (2005) and by Bayati et al (2006,2008) in two different contexts, where the zero-temperature version of the BPalgorithm finds the ML solution for special models on graphs with loops. Thesetwo models share a key feature: their ML solutions can be found by an efficientlinear programming (LP) algorithm with a totally uni-modular (TUM) matrix ofconstraints. Generalizing the two models, we consider a class of graphical modelsreducible in the zero-temperature limit to LP with TUM constraints. Assuming thata gedanken algorithm, g-BP, for finding the global minimum of the Bethe freeenergy is available, we show that in the limit of zero temperature, g-BP outputsthe ML solution. Our consideration is based on equivalence established betweengapless linear programming (LP) relaxation of the graphical model in the T → 0 limit and the respective LP version of the Bethe free energy minimization.

Background. Adequate physical activity is essential to healthy aging. This study aimed to examine the construct validity of the Persian version of the Physical Activity Scale for the Elderly (PASE) among community-dwelling adults, which would be used as a screening tool at the Neyshabur longitudinal study on the aging (NELSA) Center. Methods. This cross-sectional study was conducted in Neyshabur, Iran, as a pilot phase at the NELSA center between May and January 2019. The sampling method was a stratified random method. For explanatory factor analysis (EFA) and confirmatory factor analysis (CFA), 300 and 650 community-dwelling adults aged 50 and older were selected, respectively. EFA was used with the principal component extraction method, and Varimax rotation and CFA were performed with the maximum likelihood estimation method. Results. Of the 950 participants, 445 (46.8%) were male, and 505 (53.2%) were female. The mean age of participants was 63 ± 8.6 years. The mean physical activity score was 89.7 ± 70.7. According to the percentage of variance explained in EFA, all five extracted factors explained 62.7% of the total variance. The results of CFA showed that all item-scale relationships were significant (P < 0.05), except for household activity (Q8) and leisure time activity (Q2) (P > 0.05). The values of the fit indices showed that the model fits well with the data. Conclusion. The EFA and CFA confirmed the construct validity of the Persian version of PASE. This questionnaire is suitable for measuring the physical activity level of older Persian adults. Practical Implications. The Persian version of PASE is suitable for measuring the physical activity level of older Persian adults.