A Primer on Fixed Effects and Fixed-Effects Panel Modeling Using R, Stata, and SPSS

Psychological data are often clustered within organizational units, which violates the independence assumption in standard regression models. Clustered errors, multilevel models, and fixed-effects models all address this issue, but in different ways. Disciplinary preferences for approaching clustered data are strong, which can restrict questions researchers ask because certain approaches are better equipped to handle particular types of questions. Resources comparing approaches to facilitate broader understanding of clustered data approaches exist for economists, political scientists, and biostatisticians. These existing resources use concepts and terminology consistent with statistical training in other disciplines, so this article provides a resource using language and principles familiar to psychologists. The article starts by walking through the origin and importance of the independence assumption to motivate the problem and emergence of different solutions in different fields. Then, information on clustered errors, multilevel models, and fixed-effect models is provided, including (a) how each approach addresses independence violations, (b) research questions ideally suited for each approach, and (c) example analyses highlighting advantages and disadvantages. The article then discusses how these approaches are not mutually exclusive but instead can be blended together to create tailor-made models that flexibly accommodate idiosyncrasies in research questions and are robust to nuances of a particular data set. The broader theme is that there is no one-size-fits-all approach to clustered data. The research question-not disciplinary preferences-should inform the statistical approach. Wider appreciation of the landscape of clustered data approaches can expand the questions researchers ask and improve the theoretical foundation of statistical models. (PsycInfo Database Record (c) 2026 APA, all rights reserved).

Structural equation modeling (SEM) is becoming the central and arguably most popular analytical tool in social sciences. Many classical and modern statistical techniques such as regression analysis, path analysis, confirmatory factor analysis, and models with both measurement and structural components have been shown to fall under the umbrella of SEM. The flexibility of SEM makes it applicable to many research designs, including experimental and non-experimental data, cross-sectional and longitudinal data, and multiple-group and multilevel problems.Recently, there have been exciting advancements in SEM, from fundamental issues like alternative estimation methods that are robust to often violated assumptions to the expansions of SEM to incorporate complex multilevel and cross-classified data that are common in the social sciences. This Research Topic aims to bring in a collection of SEM papers which not only tackle technical estimation issues, but also examine and demonstrate the applications of SEM to more complex settings. The proposed topics include (but are not limited to): applying robust estimation method, testing interaction effect, examining measurement invariance, and specifying and evaluating models applied to more complex data including meta-analytic data, multilevel and longitudinal data.

This study examined peer predictors of variation and growth in depressed mood among high-risk adolescents, using child and parent reports of monthly symptoms. One hundred seventy-six parents and their 10- to 14-year-old children separately took part in a series of up to nine monthly interviews. Multilevel growth models examined both time-varying peer predictors of parent and child reports of the child's depressive symptoms, controlling for age, gender, and treatment status. Deviant peer affiliation significantly predicted elevated depressive symptoms in the monthly child-report of depressed mood, especially for younger adolescents. Children's level of delinquency was significantly related to parent-reported depressive symptoms, and to child-reported symptoms in older adolescents only. As expected, depressed mood was higher for girls and more prevalent among older adolescents. The results suggest that peer processes may be linked in time to the development of depression, especially among high-risk adolescents.

Social and Physical Neighbourhood Environment and Risk of Depression in Adults With Diabetes

Background Addressing the impact of poverty through income and welfare policies is likely important for public mental health; however, few studies assess potential effect size using causally-informed methodologies. To provide meaningful information for policymakers, we aimed to estimate the average treatment effect of transitioning into poverty on mental health. Methods We used data for working-age adults (aged 25-64) from nine waves of the nationally representative UK Household Longitudinal Survey (2009-2019, n = 39,553 obs=155,963). Exposure was transition into poverty (household equiv. income <60% median). Outcome was score ≥4 on General Health Questionnaire-12, indicating likely common mental disorder (CMD). To minimise the influence of reverse causation and time-varying confounders we used a marginal structural modelling (MSM) approach to create inverse probability of treatment weights. We performed secondary analysis stratifying by sex, and calculated population attributable fractions for each model. Results Good balance of confounders was achieved between exposure groups. Experiencing new poverty was associated with increased odds of CMD (adjusted OR 1.33, 95% CI 1.24-1.42, p < 0.001) with a 4.8% (3.6-6.0) absolute difference in prevalence: 24.0% vs 19.2%. There was a difference in relative effect by sex, with OR 1.40 (1.25-1.56, p < 0.001) for men vs OR 1.28 (1.18-1.38, p < 0.001) for women. However, there was no marked difference in absolute effect by sex: 4.9% (3.1-6.8) for men vs 4.5% (3.0-6.1) for women. For all analyses traditional logistic regression using the same confounders underestimated the effect in comparison with MSM. Conclusions Moving below the poverty line increased odds of CMD by 32.7% after accounting for confounding and reverse causality, with a greater relative impact on men. Our causal estimates suggest transition into poverty currently accounts for 10.7% of the burden of CMD in the UK working-age population - 8.9% for women and 13.1% for men. Key messages Reductions in household income worsen mental health, and traditional analytical approaches may be underestimating this causal relationship. Applying causal methodologies to observational data can provide exposure-outcome estimates less susceptible to common biases, which may be of more use to policymakers.

Correlation or causation? Income inequality and infant mortality in fixed effects models in the period 1960–2008 in 34 OECD countries

Background: Low vitamin B-6 status has been linked to depressive symptomatology. However, most studies have been cross-sectional and may not have controlled for relevant confounders. Few studies have examined this association in Latino populations at high risk for major depression. Design: We used two-level hierarchical linear regression models (HLM) for continuous outcomes. Level-1 data included three measures of participant’s depressive symptomatology collected at baseline, 2y follow-up and 5y follow-up. Participants constituted level-2 data. Vitamin B-6 was associated with depressive symptomatology across these time points. Objective: We examined the longitudinal association of vitamin B-6 status with depressive symptomatology across 3 time points over ~ 5-7 y in a cohort of older Puerto Rican adults, a population previously identified to be at high risk for depressive symptomatology and clinical depression. Results: Plasma pyridoxyl-5’-phosphate (PLP) concentration, a time-varying predictor, was significantly associated with depressive symptomatology. Study participants with PLP deficiency, vs. optimal PLP, had higher baseline depressive symptoms (22±14, vs. 20±13); this differential remained constant over time and persisted after controlling for age, sex, education, BMI, smoking and alcohol use, other relevant nutritional factors, perceived stress, stressful life events and allostatic load; and use of antidepressant medication. However, PLP concentration was not associated with the rate of change in depressive symptomatology over time. Conclusions: Suboptimal plasma PLP is associated with higher depressive symptomatology in older Puerto Rican adults and this appears to persist over time. Our data suggest that identification and treatment of vitamin B-6 deficiency may be a useful preventive and intervention approach in this population.

Addressing the policy challenges and opportunities of “Big data”

With rapid urbanization and intensive rural-urban migration, being overweight has become an increasingly common source of health risks in low- and middle-income countries (LMICs). However, the impact of rural-urban migration on overweight status is understudied in the LMIC context. Previous studies primarily used cross-sectional data, failing to adjust for migration health selection. Furthermore, the potential gender pattern in the impact of rural-urban migration remained unclear, and the potential cumulative effect of the duration of urban residence among migrants was rarely examined with longitudinal data. Meanwhile, the mediating effects of health behavioral factors were poorly understood. Using data from the fourth and fifth waves of the Indonesia Family Life Survey (IFLS) and employing fixed-effects (FE) models (N=7267), this study provided new evidence on the impact of rural-urban migration on overweight status across time and gender. Findings suggest that rural-urban migration significantly and positively predicted being overweight, and the association was significantly stronger among women than men. The results also show that years lived in urban areas did not significantly predict overweight among migrants, and that mediating health-related behaviors did little to explain adverse weight outcomes of migrants. As the number of rural-urban migrants continues growing, LMIC governments should implement health interventions aiming for healthy weight status among migrant communities. Meanwhile, gender-specific programs targeting women should be considered. Future research should explore other potential mediators of the link between rural-urban migration and overweight.

The purpose of this research was to compare the performances of the Fixed Effect Model (FEM) and the Random Effects Model (REM) in the meta-analysis studies conducted through 5, 10, 20 and 40 studies with an outlier and 4, 9, 19 and 39 studies without an outlier in terms of estimated common effect size, confidence interval coverage rate and heterogeneity measures. In this descriptive study, real data set consisting of different studies examining teachers’ emotional burnout in terms of gender were used and a total of 72 meta-analyses were performed with R program. The results indicated that REM was more advantageous when compared to FEM for the meta-analysis of data sets with an outlier. On the other hand, without an outlier, it was determined that the common effect size was generally estimated to be similar for all methods. Moreover, the increase in the number of studies included in the meta-analysis reduced the effect of the outlier on the effect size estimation and decreased the heterogeneity. When the examination of the confidence interval coverage accuracy rates of the meta-analysis methods was examined, it was concluded that the confidence intervals included the estimated effect sizes in all data sets and all methods. The findings of the current study showed that the methods used in meta-analysis studies with 20 or more studies were less affected by the outlier runs in the estimated common effect size.

Observed associations of alcohol with colorectal cancer are prone to distortion by confounding and reverse causation. A Mendelian randomization approach provides an unbiased estimate of the association using the aldehyde dehydrogenase 2 (ALDH2) variant as a surrogate of alcohol exposure. A meta-analysis was performed to assess the association between the ALDH2 genotype and colorectal neoplasia, using the ALDH2 genotype as a marker of alcohol intake. The pooled odds ratio (OR) of colorectal neoplasia was 1.31 (95%CI, 1.01-1.70) for the Glu/Glu vs the Lys/Lys genotype. There was no evidence of interstudy heterogeneity (P = 0.12, I² = 42.7). The overall risk for Glu/Lys heterozygotes relative to Lys/Lys homozygotes (under a fixed-effects model) was 1.13 (95%CI, 0.86-1.48). There was no evidence of publication bias for Glu/Glu or Glu/Lys analysis. The result supports the role of alcohol in colorectal carcinogenesis based on a Mendelian randomization approach.

Pioglitazone, a thiazolidinedione, effectively reduces stroke and cardiovascular events in individuals with type 2 diabetes, insulin resistance, and/or stroke. However, its potential to increase fracture risk, particularly among women and those with pre-existing skeletal conditions, has not yet been completely understood. This meta-analysis aims to clarify fracture risk associated with pioglitazone, thereby focusing on individuals with a history of stroke. A systematic review was performed for clinical trials conducted up to March 2024, focusing on trials comparing pioglitazone to placebo or other antihyperglycemic drugs that reported fracture outcomes. From 860 trials identified, 78 satisfied the inclusion criteria: 34 with a high risk of bias, 8 with unclear risk, and 36 with low risk. The meta-analysis revealed an association between pioglitazone and a significant increase in fracture risk (risk ratio [RR] 1.21; 95% CI 1.01-1.45; P = 0.04), including non-serious (RR 1.25; 95% CI 1.03-1.51; P = 0.02) and serious fractures (RR 1.48; 95% CI 1.10-1.98; P = 0.01). Notably, the risk was exacerbated for low-energy fractures, particularly resulting from falls (RR 1.49; 95% CI 1.20-1.87; P = 0.0004), in insulin resistance individuals (RR 0.87; 95% CI 0.43-1.76; P = 0.69), and stroke survivors (RR 1.41; 95% CI 1.09-1.83; P = 0.008). Fractures were most frequently observed in lower extremities (RR 1.85; 95% CI 1.33-2.56; P = 0.0002), with women at a greater risk (RR 1.56; 95% CI 1.20-2.02; P = 0.0008). When compared with other antihyperglycemic drugs, no significant difference in fracture risk was noted (RR 1.08; 95% CI 0.73-1.59; P = 0.70), except rosiglitazone, which showed higher fracture risk (RR 1.42; 95% CI 1.23-1.64; P < 0.00001). Fracture risk was significant in the fixed-effect model but not in the random-effects model. Though pioglitazone offers several cardiovascular benefits, its association with increased fracture risk, especially among women and non-diabetic individuals post-stroke, warrants careful consideration. Individualized treatment interventions balancing cardiovascular and skeletal outcomes are essential, and further research is needed to optimize therapeutic strategies in this population. https://www.crd.york.ac.uk/PROSPERO/display_record.php?ID=CRD42016038242, identifier CRD42016038242.

Prevalence and Risk Factors for Depression in a Longitudinal, Population-Based Study Including Individuals in the Community and Residential Care

BackgroundThe relative importance of income, poverty and unemployment status for mental health is unclear, and understanding this has implications for income and welfare policy design. We aimed to assess the association between changes in these exposures and mental health. MethodsWe measured effects of three transition exposures between waves of the UK Household Longitudinal Study from 2010/11–2019/20 (n=38,697, obs=173,859): income decreases/increases, moving in/out of poverty, and job losses/gains. The outcome was General Health Questionnaire (GHQ), which measures likelihood of common mental disorder (CMD) as a continuous (GHQ-36) and binary measure (score ≥4 = case). We used fixed-effects linear and linear probability models to adjust for time invariant and time-varying confounders. To investigate effect modification, we stratified analyses by age, sex and highest education. ResultsA 10% income decrease/increase was associated with a 0.02% increase (95% CI 0.00, 0.04) and 0.01% reduction (95% CI -0.03, 0.02) in likelihood of CMD respectively. Effect sizes were larger for moving into poverty (+1.8% [0.2, 3.5]), out of poverty (−1.8%, [-3.2, −0.3]), job loss (+15.8%, [13.6, 18.0]) and job gain (−11.4%, [-14.4, −8.4]). The effect of new poverty was greater for women (+2.3% [0.8, 3.9] versus +1.2% [-1.1, 3.5] for men) but the opposite was true for job loss (+17.8% [14.4, 21.2] for men versus +13.5% [9.8, 17.2] for women). There were no clear differences by age, but those with least education experienced the largest effects from poverty transitions, especially moving out of poverty (−2.9%, [-5.7, −0.0]). ConclusionsMoving into unemployment was most strongly associated with CMD, with poverty also important but income effects generally much smaller. Men appear most sensitive to employment transitions, but poverty may have larger impacts on women and those with least education. As the COVID-19 pandemic recedes, minimising unemployment as well as poverty is crucial for population mental health.

This investigation examines the efficacy of multilevel analysis of individual heterogeneity and discriminatory accuracy (MAIHDA) over fixed-effects models when performing intersectional studies. The research questions are as follows: (1) What are typical strata representation rates and outcomes on physics research-based assessments? (2) To what extent do MAIHDA models create more accurate predicted strata outcomes than fixed-effects models? and (3) To what extent do MAIHDA models allow the modeling of smaller strata sample sizes? We simulated 3,000 data sets based on real-world data from 5,955 students on the LASSO platform. We found that MAIHDA created more accurate and precise predictions than fixed-effects models. We also found that using MAIHDA could allow researchers to disaggregate their data further, creating smaller group sample sizes while maintaining more accurate findings than fixed-effects models. We recommend using MAIHDA over fixed-effects models for intersectional investigations.