Current practice in factor analysis typically involves analysis of correlation rather than covariance matrices. We study whether the standard z-statistic that evaluates whether a factor loading is statistically necessary is correctly applied in such situations and more generally when the variables being analyzed are arbitrarily rescaled. Effects of rescaling on estimated standard errors of factor loading estimates, and the consequent effect on z-statistics, are studied in three variants of the classical exploratory factor model under canonical, raw varimax, and normal varimax solutions. For models with analytical solutions we find that some of the standard errors as well as their estimates are scale equivariant, while others are invariant. For a model in which an analytical solution does not exist, we use an example to illustrate that neither the factor loading estimates nor the standard error estimates possess scale equivariance or invariance, implying that different conclusions could be obtained with different scalings. Together with the prior findings on parameter estimates, these results provide new guidance for a key statistical aspect of factor analysis.

A paradoxical implication of Kraemer's expression for the large-sample standard error of Brogden's form of the biserial correlation is identified, and a new expression is given which does not imply the paradox. However, numerical evidence is presented which calls into question the correctness of the expression.

It is shown that the PAR Derivative-Free Nonlinear Regression program in BMDP can be used to fit structural equation models, producing generalized least squares estimates, standard errors, and goodness-of-fit test statistics. Covariance structure models more general than LISREL can be analyzed. The approach is particularly useful for dealing with new non-standard models and experimenting with alternate methods of estimation.

Exploratory process factor analysis (EPFA) is a data-driven latent variable model for multivariate time series. This article presents analytic standard errors for EPFA. Unlike standard errors for exploratory factor analysis with independent data, the analytic standard errors for EPFA take into account the time dependency in time series data. In addition, factor rotation is treated as the imposition of equality constraints on model parameters. Properties of the analytic standard errors are demonstrated using empirical and simulated data.

The infinitesimal jackknife, a nonparametric method for estimating standard errors, has been used to obtain standard error estimates in covariance structure analysis. In this article, we adapt it for obtaining standard errors for rotated factor loadings and factor correlations in exploratory factor analysis with sample correlation matrices. Both maximum likelihood estimation and ordinary least squares estimation are considered.

This paper analyzes the sum score based (SSB) formulation of the Rasch model, where items and sum scores of persons are considered as factors in a logit model. After reviewing the evolution leading to the equality between their maximum likelihood estimates, the SSB model is then discussed from the point of view of pseudo-likelihood and of misspecified models. This is then employed to provide new insights into the origin of the known inconsistency of the difficulty parameter estimates in the Rasch model. The main results consist of exact relationships between the estimated standard errors for both models; and, for the ability parameters, an upper bound for the estimated standard errors of the Rasch model in terms of those for the SSB model, which are more easily available.

In this paper we propose an upward correction to the standard error (SE) estimation of \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$\hat{\theta}_{\mathrm{ML}}$\end{document}, the maximum likelihood (ML) estimate of the latent trait in item response theory (IRT). More specifically, the upward correction is provided for the SE of \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$\hat{\theta}_{\mathrm{ML}}$\end{document} when item parameter estimates obtained from an independent pretest sample are used in IRT scoring. When item parameter estimates are employed, the resulting latent trait estimate is called pseudo maximum likelihood (PML) estimate. Traditionally, the SE of \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$\hat{\theta}_{\mathrm{ML}}$\end{document} is obtained on the basis of test information only, as if the item parameters are known. The upward correction takes into account the error that is carried over from the estimation of item parameters, in addition to the error in latent trait recovery itself. Our simulation study shows that both types of SE estimates are very good when θ is in the middle range of the latent trait distribution, but the upward-corrected SEs are more accurate than the traditional ones when θ takes more extreme values.

In computerized adaptive testing (CAT), a variable-length stopping rule refers to ending item administration after a pre-specified measurement precision standard has been satisfied. The goal is to provide equal measurement precision for all examinees regardless of their true latent trait level. Several stopping rules have been proposed in unidimensional CAT, such as the minimum information rule or the maximum standard error rule. These rules have also been extended to multidimensional CAT and cognitive diagnostic CAT, and they all share the same idea of monitoring measurement error. Recently, Babcock and Weiss (J Comput Adapt Test 2012. https://doi.org/10.7333/1212-0101001) proposed an “absolute change in theta” (CT) rule, which is useful when an item bank is exhaustive of good items for one or more ranges of the trait continuum. Choi, Grady and Dodd (Educ Psychol Meas 70:1–17, 2010) also argued that a CAT should stop when the standard error does not change, implying that the item bank is likely exhausted. Although these stopping rules have been evaluated and compared in different simulation studies, the relationships among the various rules remain unclear, and therefore there lacks a clear guideline regarding when to use which rule. This paper presents analytic results to show the connections among various stopping rules within both unidimensional and multidimensional CAT. In particular, it is argued that the CT-rule alone can be unstable and it can end the test prematurely. However, the CT-rule can be a useful secondary rule to monitor the point of diminished returns. To further provide empirical evidence, three simulation studies are reported using both the 2PL model and the multidimensional graded response model.

This paper studies changes of standard errors (SE) of the normal-distribution-based maximum likelihood estimates (MLE) for confirmatory factor models as model parameters vary. Using logical analysis, simplified formulas and numerical verification, monotonic relationships between SEs and factor loadings as well as unique variances are found. Conditions under which monotonic relationships do not exist are also identified. Such functional relationships allow researchers to better understand the problem when significant factor loading estimates are expected but not obtained, and vice versa. What will affect the likelihood for Heywood cases (negative unique variance estimates) is also explicit through these relationships. Empirical findings in the literature are discussed using the obtained results.

This study revisits the parameter estimation issues in multidimensional item response theory more thoroughly and investigates some computation details that have seldom been addressed previously when implementing the expectation-maximization (EM) algorithm for finite mixtures (EM–FM). Two research questions are: Should we rescale after each EM cycle or after the final EM cycle? How to adapt the supplemented EM algorithm to the EM–FM framework to estimate standard errors (SEs) of all unknown parameters? Analytic details of the methods are provided, and a comprehensive simulation study is conducted to provide supporting evidence. Results reveal that rescaling after each EM cycle accelerates convergence without affecting the calibration accuracy. Moreover, the SEs of all model parameters, including item parameters and population mixing proportions, recover well when the sample size is relatively large (e.g., 2000).

While estimation bias is a primary concern in psychological and educational measurement, the standard error is of equal importance in linking key aspects of the assessment structure, especially when the assessment goal concerns the classification of individuals into categories (e.g., master/non-mastery). In this paper, we show analytically how standard error of ability estimates affects expected classification accuracy and consistency when the decision is binary. When standard error decreases, the conditional classification accuracy and consistency increase. Given an examinee population and a cut score, smaller standard error over the entire latent trait continuum guarantees higher overall expected classification accuracy and consistency. We were also able to show the interrelationship between standard error, the expected classification consistency, and reliability. Utilizing the relationship between standard error and expected classification accuracy and consistency, we derive the upper bounds of the overall expected classification accuracy and consistency of a fixed-length computerized adaptive test. The lower bound of the expected classification accuracy and consistency is also derived given a number of stopping rules of variable-length computerized adaptive testing. Implications of these analytical results on operational tests are discussed.

The social defeat hypothesis posits that low status and repeated humiliation increase the risk for psychotic disorders (PDs) and psychotic experiences (PEs). The purpose of this paper was to provide a systematic review of studies on risk of PDs and PEs among lesbian, gay, or bisexual (LGB) people and a quantitative synthesis of any difference in risk. PubMed, PsycINFO, Embase, and Web of Science were searched from database inception until January 30, 2024. Two independent reviewers assessed the eligibility and quality of studies, extracted effect sizes, and noted the results of mediation analyses. Using a random effects model we computed pooled odds ratios (ORs). Preferred Reporting Items for Systematic Reviews and Meta-Analyses guidelines were followed. The search identified seven studies of PDs and six of PEs. As for PDs, the unadjusted (2.13; 95% confidence interval 0.72–6.34) and covariate-adjusted pooled OR (2.24; 1.72–3.53) were not significantly increased for LGB individuals. After exclusion of a study of limited quality, both the unadjusted pooled OR (2.77; 1.21–6.32) and the covariate-adjusted pooled OR (2.67; 1.53–4.66) were significantly increased. The pooled ORs were increased for PEs: unadjusted, pooled OR = 1.97 (1.47–2.63), covariate-adjusted, pooled OR = 1.85 (1.50–2.28). Studies of PE that examined the mediating role of several variables reported that the contribution of drug abuse was small compared to that of psychosocial stressors. The results of a study in adolescents suggested a protective effect of parental support. These findings suggest an increased psychosis risk for LGB people and support the social defeat hypothesis.

Food insecurity, poised to increase with burgeoning concerns related to climate change, may influence sleep, yet few studies examined the food security-sleep association among racially/ethnically diverse populations with multiple sleep dimensions. We determined overall and racial/ethnic-specific associations between food security and sleep health. Using National Health Interview Survey data, we categorised food security as very low, low, marginal and high. Sleep duration was categorised as very short, short, recommended and long. Sleep disturbances included trouble falling/staying asleep, insomnia symptoms, waking up feeling unrested and using sleep medication (all ≥3 d/times in the previous week). Adjusting for socio-demographic characteristics and other confounders, we used Poisson regression with robust variance to estimate prevalence ratios (PRs) and 95 % confidence intervals (95 % CIs) for sleep dimensions by food security. Among 177 435 participants, the mean age of 47⋅2 ± 0⋅1 years, 52⋅0 % were women, and 68⋅4 % were non-Hispanic (NH)-White. A higher percent of NH-Black (7⋅9 %) and Hispanic/Latinx (5⋅1 %) lived in very low food security households than NH-White (3⋅1 %) participants. Very low v. high food security was associated with a higher prevalence of very short (PR = 2⋅61 [95 % CI 2⋅44–2⋅80]) sleep duration as well as trouble falling asleep (PR = 2⋅21 [95 % CI 2⋅12–2⋅30]). Very low v. high food security was associated with a higher prevalence of very short sleep duration among Asian (PR = 3⋅64 [95 % CI 2⋅67–4⋅97]) and NH-White (PR = 2⋅73 [95 % CI 2⋅50–2⋅99]) participants compared with NH-Black (PR = 2⋅03 [95 % CI 1⋅80–2⋅31]) and Hispanic/Latinx (PR = 2⋅65 [95 % CI 2⋅30–3⋅07]) participants. Food insecurity was associated with poorer sleep in a racially/ethnically diverse US sample.

We sought to examine the effects of daily consumption of macadamia nuts on body weight and composition, plasma lipids and glycaemic parameters in a free-living environment in overweight and obese adults at elevated cardiometabolic risk. Utilising a randomised cross-over design, thirty-five adults with abdominal obesity consumed their usual diet plus macadamia nuts (~15 % of daily calories) for 8 weeks (intervention) and their usual diet without nuts for 8 weeks (control), with a 2-week washout. Body composition was determined by bioelectrical impedance; dietary intake was assessed with 24-h dietary recalls. Consumption of macadamia nuts led to increased total fat and MUFA intake while SFA intake was unaltered. With mixed model regression analysis, no significant changes in mean weight, BMI, waist circumference, percent body fat or glycaemic parameters, and non-significant reductions in plasma total cholesterol of 2⋅1 % (−4⋅3 mg/dl; 95 % CI −14⋅8, 6⋅1) and low-density lipoprotein (LDL-C) of 4 % (−4⋅7 mg/dl; 95 % CI −14⋅3, 4⋅8) were observed. Cholesterol-lowering effects were modified by adiposity: greater lipid lowering occurred in those with overweight v. obesity, and in those with less than the median percent body fat. Daily consumption of macadamia nuts does not lead to gains in weight or body fat under free-living conditions in overweight or obese adults; non-significant cholesterol lowering occurred without altering saturated fat intake of similar magnitude to cholesterol lowering seen with other nuts.

Clinical Trial Registry Number and Website: NCT03801837 https://clinicaltrials.gov/ct2/show/NCT03801837?term = macadamia + nut&draw = 2&rank = 1

Complete nutrition drinks with a low glycemic index (GI) provide nutritional support and prevent hyperglycaemia. The present study identified GI and factors predicting individual glucose response to a new complete nutrition drink. A randomised cross-over controlled trial was conducted in eighteen healthy volunteers (FPG < 100 mg/dl). Complete nutrition drinks containing retrograded starch, glucose solution and white bread were assigned in a random sequence with 14-day wash-out intervals. Plasma glucose and insulin levels were measured from baseline to 180 min after consuming each food. Results show the adjusted GIs of the drink was 48.2 ± 10.4 and 46.7 ± 12.7 with glucose and white bread as the reference, respectively. While the drink has low GI (<55), the individual glucose responses varied (GI: 7–149). Comparing characters in individual GI < 55 (n = 12) and GI ≥ 55 (n = 6) groups revealed significantly higher baseline insulin in the low GI group (14.86 ± 16.51 μIU/ml v. 4.9 ± 3.4 μIU/ml, P < 0·05). The correlation matrix confirms only two predictive factors for having individual GI <55 were baseline insulin (r = 0·5, P = 0·03) and HOMA-IR (r = 0·55, P = 0·02). ROC curve reveals fasting insulin above 1.6 μIU/ml and HOMA-IR above 1.05 as the cut-off values. The findings suggest that the complete nutrition drink has a low GI, but there was wide variability in individual responses partly explained by fasting insulin levels and HOMA-IR. Screening for fasting insulin and HOMA-IR may be encouraged to maximise the functional benefit of the drink.

Stress is the most important proximal precipitant of depression, yet most large genome-wide association studies (GWAS) do not include stress as a variable. Here, we review how gene × environment (G × E) interaction might impede the discovery of genetic factors, discuss two examples of G × E interaction in depression and addiction, studies incorporating high-stress environments, as well as upcoming waves of genome-wide environment interaction studies (GWEIS). We discuss recent studies which have shown that genetic distributions can be affected by social factors such as migrations and socioeconomic background. These distinctions are not just academic but have practical consequences. Owing to interaction with the environment, genetic predispositions to depression should not be viewed as unmodifiable destiny. Patients may genetically differ not just in their response to drugs, as in the now well-recognised field of pharmacogenetics, but also in how they react to stressful environments and how they are affected by behavioural therapies.

This reflection presents a discussion of some common measures of variability and how they are appropriately used in descriptive and inferential statistical analyses. We argue that confidence intervals (CIs), which incorporate these measures, serve as tools to assess both clinical and statistical significance.

ANOVA, one of the most common statistical methods applied in agronomy, offers a variety of results we can report when analyzing designed experiments. The focus, of course, is on treatment means, but what should we report to characterize precision? Should we choose treatment standard deviations (SDs) or standard errors of the mean or standard errors of the difference (SEDs)? We discuss why treatment raw SDs should not be reported as the result of ANOVA, and point out that most of the time it is SEDs that should be provided.