Power analyses for measurement model misspecification and response shift detection with structural equation modeling.

PURPOSE: Statistical power for response shift detection with structural equation modeling (SEM) is currently underreported. The present paper addresses this issue by providing worked-out examples and syntaxes of power calculations relevant for the statistical tests associated with the SEM approach for response shift detection. METHODS: Power calculations and related sample-size requirements are illustrated for two modelling goals: (1) to detect misspecification in the measurement model, and (2) to detect response shift. Power analyses for hypotheses regarding (exact) overall model fit and the presence of response shift are demonstrated in a step-by-step manner. The freely available and user-friendly R-package lavaan and shiny-app 'power4SEM' are used for the calculations. RESULTS: Using the SF-36 as an example, we illustrate the specification of null-hypothesis (H0) and alternative hypothesis (H1) models to calculate chi-square based power for the test on overall model fit, the omnibus test on response shift, and the specific test on response shift. For example, we show that a sample size of 506 is needed to reject an incorrectly specified measurement model, when the actual model has two-medium sized cross loadings. We also illustrate power calculation based on the RMSEA index for approximate fit, where H0 and H1 are defined in terms of RMSEA-values. CONCLUSION: By providing accessible resources to perform power analyses and emphasizing the different power analyses associated with different modeling goals, we hope to facilitate the uptake of power analyses for response shift detection with SEM and thereby enhance the stringency of response shift research.

Evaluating SEM Model Fit with Small Degrees of Freedom.

Research has revealed that the performance of root mean square error of approximation (RMSEA) in assessing structural equation models with small degrees of freedom (df) is suboptimal, often resulting in the rejection of correctly specified or closely fitted models. This study investigates the performance of standardized root mean square residual (SRMR) and comparative fit index (CFI) in small df models with various levels of factor loadings, sample sizes, and model misspecifications. We find that, in comparison with RMSEA, population SRMR and CFI are less susceptible to the effects of df. In small df models, the sample SRMR and CFI could provide more useful information to differentiate models with various levels of misfit. The confidence intervals and p-values of a close fit were generally accurate for all three fit indices. We recommend researchers use caution when interpreting RMSEA for models with small df and to rely more on SRMR and CFI.

Improving Fit Indices in Structural Equation Modeling with Categorical Data.

Current computations of commonly used fit indices in structural equation modeling (SEM), such as RMSEA and CFI, indicate much better fit when the data are categorical than if the same data had not been categorized. As a result, researchers may be led to accept poorly fitting models with greater frequency when data are categorical. In this article, I first explain why the current computations of categorical fit indices lead to this problematic behavior. I then propose and evaluate alternative ways to compute fit indices with categorical data. The proposed computations approximate what the fit index values would have been had the data not been categorized. The developments in this article are for the DWLS (diagonally weighted least squares) estimator, a popular limited information categorical estimation method. I report on the results of a simulation comparing existing and newly proposed categorical fit indices. The results confirmed the theoretical expectation that the new indices better match the corresponding values with continuous data. The new fit indices performed well across all studied conditions, with the exception of binary data at the smallest studied sample size (N = 200), when all categorical fit indices performed poorly.

On the Computation of the RMSEA and CFI from the Mean-And-Variance Corrected Test Statistic with Nonnormal Data in SEM.

A new type of nonnormality correction to the RMSEA has recently been developed, which has several advantages over existing corrections. In particular, the new correction adjusts the sample estimate of the RMSEA for the inflation due to nonnormality, while leaving its population value unchanged, so that established cutoff criteria can still be used to judge the degree of approximate fit. A confidence interval (CI) for the new robust RMSEA based on the mean-corrected ("Satorra-Bentler") test statistic has also been proposed. Follow up work has provided the same type of nonnormality correction for the CFI (Brosseau-Liard & Savalei, 2014). These developments have recently been implemented in lavaan. This note has three goals: a) to show how to compute the new robust RMSEA and CFI from the mean-and-variance corrected test statistic; b) to offer a new CI for the robust RMSEA based on the mean-and-variance corrected test statistic; and c) to caution that the logic of the new nonnormality corrections to RMSEA and CFI is most appropriate for the maximum likelihood (ML) estimator, and cannot easily be generalized to the most commonly used categorical data estimators.

Workplace nutrition knowledge questionnaire: psychometric validation and application.

Workplace dietary intervention studies in low- and middle-income countries using psychometrically sound measures are scarce. This study aimed to validate a nutrition knowledge questionnaire (NQ) and its utility in evaluating the changes in knowledge among participants of a Nutrition Education Program (NEP) conducted at the workplace. A NQ was tested for construct validity, internal consistency and discriminant validity. It was applied in a NEP conducted at six workplaces, in order to evaluate the effect of an interactive or a lecture-based education programme on nutrition knowledge. Four knowledge domains comprising twenty-three items were extracted in the final version of the NQ. Internal consistency of each domain was significant, with Kuder-Richardson formula values>0·60. These four domains presented a good fit in the confirmatory factor analysis. In the discriminant validity test, both the Expert and Lay groups scored>0·52, but the Expert group scores were significantly higher than those of the Lay group in all domains. When the NQ was applied in the NEP, the overall questionnaire scores increased significantly because of the NEP intervention, in both groups (P<0·001). However, the increase in NQ scores was significantly higher in the interactive group than in the lecture group, in the overall score (P=0·008) and in the healthy eating domain (P=0·009). The validated NQ is a short and useful tool to assess gain in nutrition knowledge among participants of NEP at the workplace. According to the NQ, an interactive nutrition education had a higher impact on nutrition knowledge than a lecture programme.

Examining associations between dietary patterns and metabolic CVD risk factors: a novel use of structural equation modelling.

The association between dietary patterns and metabolic cardiovascular risk factors has long been addressed but there is a lack of evidence towards the effects of the overall diet on the complex net of biological inter-relationships between risk factors. This study aimed to derive dietary patterns and examine their associations with metabolic cardiovascular risk factors following a theoretic model for the relationship between them. Participants included 417 adults of both sexes, enrolled to the cross-sectional population-based study performed in Brazil. Body weight, waist circumference, high-sensitivity C-reactive protein, blood pressure, total cholesterol:HDL-cholesterol ratio, TAG:HDL-cholesterol ratio, fasting plasma glucose and serum leptin were evaluated. Food consumption was assessed by two non-consecutive 24-h dietary recalls adjusted for the within-person variation of intake. A total of three dietary patterns were derived by exploratory structural equation modelling: 'Traditional', 'Prudent' and 'Modern'. The 'Traditional' pattern had a negative and direct effect on obesity indicators (serum LEP, body weight and waist circumference) and negative indirect effects on total cholesterol:HDL-cholesterol ratio, TAG:HDL-cholesterol ratio and fasting plasma glucose. The 'Prudent' pattern had a negative and direct effect on systolic blood pressure. No association was observed for the 'Modern' pattern and metabolic risk factors. In conclusion, the 'Traditional' and 'Prudent' dietary patterns were negatively associated with metabolic cardiovascular risk factors among Brazilian adults. Their apparent protective effects against obesity and high blood pressure may be important non-pharmacological strategies for the prevention and control of obesity-related metabolic disorders and CVD.

Evaluating Structural Equation Models for Categorical Outcomes: A New Test Statistic and a Practical Challenge of Interpretation.

This research is concerned with two topics in assessing model fit for categorical data analysis. The first topic involves the application of a limited-information overall test, introduced in the item response theory literature, to structural equation modeling (SEM) of categorical outcome variables. Most popular SEM test statistics assess how well the model reproduces estimated polychoric correlations. In contrast, limited-information test statistics assess how well the underlying categorical data are reproduced. Here, the recently introduced C2 statistic of Cai and Monroe (2014) is applied. The second topic concerns how the root mean square error of approximation (RMSEA) fit index can be affected by the number of categories in the outcome variable. This relationship creates challenges for interpreting RMSEA. While the two topics initially appear unrelated, they may conveniently be studied in tandem since RMSEA is based on an overall test statistic, such as C2. The results are illustrated with an empirical application to data from a large-scale educational survey.

Using the Bollen-Stine Bootstrapping Method for Evaluating Approximate Fit Indices.

Accepting that a model will not exactly fit any empirical data, global approximate fit indices quantify the degree of misfit. Recent research (Chen et al., 2008) has shown that using fixed conventional cut-points for approximate fit indices can lead to decision errors. Instead of using fixed cut-points for evaluating approximate fit indices, this study focuses on the meaning of approximate fit and introduces a new method to evaluate approximate fit indices. Millsap (2012) introduced a simulation-based method to evaluate approximate fit indices. A limitation of Millsap's work was that a rather strong assumption of multivariate normality was implied in generating simulation data. In this study, the Bollen-Stine bootstrapping procedure (Bollen & Stine, 1993) is proposed to supplement the former study. When data are non-normal, the conclusions derived from Millsap's (2012) simulation method and the Bollen-Stine method can differ. Examples are given to illustrate the use of the Bollen-Stine bootstrapping procedure for evaluating RMSEA. Comparisons are made with the simulation method. The results are discussed, and suggestions are given for the use of proposed method.

Using Structural Equation Modeling to Assess Functional Connectivity in the Brain: Power and Sample Size Considerations.

The present study assessed the impact of sample size on the power and fit of structural equation modeling applied to functional brain connectivity hypotheses. The data consisted of time-constrained minimum norm estimates of regional brain activity during performance of a reading task obtained with magnetoencephalography. Power analysis was first conducted for an autoregressive model with 5 latent variables (brain regions), each defined by 3 indicators (successive activity time bins). A series of simulations were then run by generating data from an existing pool of 51 typical readers (aged 7.5-12.5 years). Sample sizes ranged between 20 and 1,000 participants and for each sample size 1,000 replications were run. Results were evaluated using chi-square Type I errors, model convergence, mean RMSEA (root mean square error of approximation) values, confidence intervals of the RMSEA, structural path stability, and D-Fit index values. Results suggested that 70 to 80 participants were adequate to model relationships reflecting close to not so close fit as per MacCallum et al.'s recommendations. Sample sizes of 50 participants were associated with satisfactory fit. It is concluded that structural equation modeling is a viable methodology to model complex regional interdependencies in brain activation in pediatric populations.

Comparing RMSEA-Based Indices for Assessing Measurement Invariance in Confirmatory Factor Models.

Fit indices are descriptive measures that can help evaluate how well a confirmatory factor analysis (CFA) model fits a researcher's data. In multigroup models, before between-group comparisons are made, fit indices may be used to evaluate measurement invariance by assessing the degree to which multiple groups' data are consistent with increasingly constrained nested models. One such fit index is an adaptation of the root mean square error of approximation (RMSEA) called RMSEAD. This index embeds the chi-square and degree-of-freedom differences into a modified RMSEA formula. The present study comprehensively compared RMSEAD to ΔRMSEA, the difference between two RMSEA values associated with a comparison of nested models. The comparison consisted of both derivations as well as a population analysis using one-factor CFA models with features common to those found in practical research. The findings demonstrated that for the same model, RMSEAD will always have increased sensitivity relative to ΔRMSEA with an increasing number of indicator variables. The study also indicated that RMSEAD had increased ability to detect noninvariance relative to ΔRMSEA in one-factor models. For these reasons, when evaluating measurement invariance, RMSEAD is recommended instead of ΔRMSEA.

Evaluating Close Fit in Ordinal Factor Analysis Models With Multiply Imputed Data.

Multiple imputation (MI) is one of the recommended techniques for handling missing data in ordinal factor analysis models. However, methods for computing MI-based fit indices under ordinal factor analysis models have yet to be developed. In this short note, we introduced the methods of using the standardized root mean squared residual (SRMR) and the root mean square error of approximation (RMSEA) to assess the fit of ordinal factor analysis models with multiply imputed data. Specifically, we described the procedure for computing the MI-based sample estimates and constructing the confidence intervals. Simulation results showed that the proposed methods could yield sufficiently accurate point and interval estimates for both SRMR and RMSEA, especially in conditions with larger sample sizes, less missing data, more response categories, and higher degrees of misfit. Based on the findings, implications and recommendations were discussed.

Evaluating fit indices in a multilevel latent growth model with unbalanced design: a Monte Carlo study.

This study informed researchers about the performance of different level-specific and target-specific model fit indices in the Multilevel Latent Growth Model (MLGM) with unbalanced design. As the use of MLGMs is relatively new in applied research domain, this study helped researchers using specific model fit indices to evaluate MLGMs. Our simulation design factors included three levels of number of groups (50, 100, and 200) and three levels of unbalanced group sizes (5/15, 10/20, and 25/75), based on simulated datasets derived from a correctly specified MLGM. We evaluated the descriptive information of the model fit indices under various simulation conditions. We also conducted ANOVA to calculated the extent to which these fit indices could be influenced by different design factors. Based on the results, we made recommendations for practical and theoretical research about the fit indices. CFI- and TFI-related fit indices performed well in the MLGM and could be trustworthy to use to evaluate model fit under similar conditions found in applied settings. However, RMSEA-related fit indices, SRMR-related fit indices, and chi square-related fit indices varied by the factors included in this study and should be used with caution for evaluating model fit in the MLGM.

Bother and distress associated with Peyronie's disease: validation of the Peyronie's disease questionnaire.

PURPOSE: We validated the Peyronie's Disease Questionnaire (http://www.auxilium.com/PDQ), a 15-question self-reported survey that measures the impact and severity of Peyronie's disease symptoms in 3 domains, including 1) psychological and physical symptoms, 2) penile pain and 3) symptom bother. MATERIALS AND METHODS: We used baseline data from 2 phase 3 clinical trials (334 and 345 patients, respectively) of collagenase clostridium histolyticum treatment for Peyronie's disease associated penile curvature and bother. Collected data included PDQ domain scores, International Index of Erectile Function scores, objective penile curvature measures and patient reported Peyronie's disease symptom severity. Psychometric analyses included confirmatory factor analysis, inter-item reliability, and tests of convergent and discriminant validity, all related to the overall construct validity of the scale. RESULTS: Confirmatory factor analysis supported the conceptual framework of the PDQ with 3 confirmed subdomains. Each scale showed good consistency, ie internal reliability (each Cronbach α >0.70). Convergent and discriminant validity were noted in the pattern of associations between PDQ domains and other Peyronie's disease measures. PDQ domain scores significantly differed between patients with vs without erectile dysfunction and between patients with vs without Peyronie's disease related symptom distress, further supporting PDQ construct validity. CONCLUSIONS: This study confirms the conceptual framework, factor structure, and convergent and discriminant validity of the PDQ psychological and physical symptoms, penile pain, and symptom bother domains. Used in conjunction with objective penile curvature measurements, the PDQ can serve as a valuable diagnostic tool or outcome measure to assess treatment related improvements in Peyronie's disease symptoms.

Scaling properties of the subjective index of physical and social outcome after stroke in a study population unselected by age.

OBJECTIVE: To investigate the scaling properties of the Subjective Index of Physical and Social Outcome (SIPSO) after stroke in survivors to hospital discharge, unselected by age. DESIGN: Factor, Mokken, and Rasch analyses of the SIPSO using data from a prospective observational cohort study. SETTING: Three acute care hospitals. PARTICIPANTS: Consecutive admissions (N=312) with acute stroke, unselected by age. INTERVENTIONS: Not applicable. MAIN OUTCOME MEASURES: Patient- or proxy-reported SIPSO, collected by postal survey 6 months after stroke. RESULTS: Complete SIPSO questionnaires were returned by 166 of 268 survivors (median age, 72y; interquartile range, 66-81y). Factor and Mokken analyses supported both 1- and 2-factor solutions. Fit to the Rasch model for the 10-item scale was poor (χ(2) test for item-trait interaction, χ(2)=69.6; P<.001). Differential item functioning by sex and age was demonstrated for the physical subscore and was dealt with through the creation of 2 super items, resulting in a good fit to the Rasch model (χ(2)=2.35; P=.67), ordered thresholds, good targeting to the latent trait, and reasonable separation reliability (Person-Separation Index, 0.8). For the social subscore, no differential item functioning was demonstrated by age or sex. Local dependence was dealt with through the creation of 2 super items. Thereafter, fit to the Rasch model (χ(2)=5.21; P=.27) and targeting to the latent trait were good, and thresholds ordered. Separation reliability was poor (Person-Separation Index, .67). CONCLUSIONS: The 10-item SIPSO is a valid ordinal scale in a population including older stroke survivors. A physical and social subscale structure is also supported. Subscales can be manipulated to fit the Rasch model, and a conversion table for conversion to an interval scale is provided. The social subscore has poor separation reliability, limiting its use in older stroke survivors.

Upper-extremity and mobility subdomains from the Patient-Reported Outcomes Measurement Information System (PROMIS) adult physical functioning item bank.

OBJECTIVE: To create upper-extremity and mobility subdomain scores from the Patient-Reported Outcomes Measurement Information System (PROMIS) physical functioning adult item bank. DESIGN: Expert reviews were used to identify upper-extremity and mobility items from the PROMIS item bank. Psychometric analyses were conducted to assess empirical support for scoring upper-extremity and mobility subdomains. SETTING: Data were collected from the U.S. general population and multiple disease groups via self-administered surveys. PARTICIPANTS: The sample (N=21,773) included 21,133 English-speaking adults who participated in the PROMIS wave 1 data collection and 640 Spanish-speaking Latino adults recruited separately. INTERVENTIONS: Not applicable. MAIN OUTCOME MEASURES: We used English- and Spanish-language data and existing PROMIS item parameters for the physical functioning item bank to estimate upper-extremity and mobility scores. In addition, we fit graded response models to calibrate the upper-extremity items and mobility items separately, compare separate to combined calibrations, and produce subdomain scores. RESULTS: After eliminating items because of local dependency, 16 items remained to assess upper extremity and 17 items to assess mobility. The estimated correlation between upper extremity and mobility was .59 using existing PROMIS physical functioning item parameters (r=.60 using parameters calibrated separately for upper-extremity and mobility items). CONCLUSIONS: Upper-extremity and mobility subdomains shared about 35% of the variance in common, and produced comparable scores whether calibrated separately or together. The identification of the subset of items tapping these 2 aspects of physical functioning and scored using the existing PROMIS parameters provides the option of scoring these subdomains in addition to the overall physical functioning score.

Measuring enfranchisement: importance of and control over participation by people with disabilities.

OBJECTIVE: To evaluate the psychometric properties and validity of an expanded set of community enfranchisement items that are suitable for computer adaptive testing. DESIGN: Survey. SETTING: Community setting. PARTICIPANTS: Individuals with disabilities (N=1163) were recruited from an online panel generation company (51%), former rehabilitation inpatients (18%), disability community organizations (13%), a registry of rehabilitation patients (10%), and Traumatic Brain Injury and Spinal Cord Injury Model System facilities (8%). Inclusion criteria were a self-identified disability, aged ≥18 years, and the ability to read and speak English. INTERVENTIONS: None. MAIN OUTCOME MEASURE: Community enfranchisement. RESULTS: Exploratory and confirmatory factor analyses of the 48 enfranchisement items suggested 2 distinct subsets of items: (1) importance of participation and (2) control over participation. Principal components analysis of the residuals suggested that the 2 item sets are unidimensional. Rating scale analysis provided evidence that the 2 item sets fit the Rasch model. Importance and control were moderately correlated with each other and with disability severity. CONCLUSIONS: Importance of participation and control over participation define 2 distinct sets of participation enfranchisement. Preliminary evidence supports their validity.

Development of a self-report physical function instrument for disability assessment: item pool construction and factor analysis.

OBJECTIVES: To build a comprehensive item pool representing work-relevant physical functioning and to test the factor structure of the item pool. These developmental steps represent initial outcomes of a broader project to develop instruments for the assessment of function within the context of Social Security Administration (SSA) disability programs. DESIGN: Comprehensive literature review; gap analysis; item generation with expert panel input; stakeholder interviews; cognitive interviews; cross-sectional survey administration; and exploratory and confirmatory factor analyses to assess item pool structure. SETTING: In-person and semistructured interviews and Internet and telephone surveys. PARTICIPANTS: Sample of SSA claimants (n=1017) and a normative sample of adults from the U.S. general population (n=999). INTERVENTIONS: Not applicable. MAIN OUTCOME MEASURE: Model fit statistics. RESULTS: The final item pool consisted of 139 items. Within the claimant sample, 58.7% were white; 31.8% were black; 46.6% were women; and the mean age was 49.7 years. Initial factor analyses revealed a 4-factor solution, which included more items and allowed separate characterization of: (1) changing and maintaining body position, (2) whole body mobility, (3) upper body function, and (4) upper extremity fine motor. The final 4-factor model included 91 items. Confirmatory factor analyses for the 4-factor models for the claimant and the normative samples demonstrated very good fit. Fit statistics for claimant and normative samples, respectively, were: Comparative Fit Index=.93 and .98; Tucker-Lewis Index=.92 and .98; and root mean square error approximation=.05 and .04. CONCLUSIONS: The factor structure of the physical function item pool closely resembled the hypothesized content model. The 4 scales relevant to work activities offer promise for providing reliable information about claimant physical functioning relevant to work disability.

Development of an instrument to measure behavioral health function for work disability: item pool construction and factor analysis.

OBJECTIVES: To develop a broad set of claimant-reported items to assess behavioral health functioning relevant to the Social Security disability determination processes, and to evaluate the underlying structure of behavioral health functioning for use in development of a new functional assessment instrument. DESIGN: Cross-sectional. SETTING: Community. PARTICIPANTS: Item pools of behavioral health functioning were developed, refined, and field tested in a sample of persons applying for Social Security disability benefits (N=1015) who reported difficulties working because of mental or both mental and physical conditions. INTERVENTIONS: None. MAIN OUTCOME MEASURE: Social Security Administration Behavioral Health (SSA-BH) measurement instrument. RESULTS: Confirmatory factor analysis (CFA) specified that a 4-factor model (self-efficacy, mood and emotions, behavioral control, social interactions) had the optimal fit with the data and was also consistent with our hypothesized conceptual framework for characterizing behavioral health functioning. When the items within each of the 4 scales were tested in CFA, the fit statistics indicated adequate support for characterizing behavioral health as a unidimensional construct along these 4 distinct scales of function. CONCLUSIONS: This work represents a significant advance both conceptually and psychometrically in assessment methodologies for work-related behavioral health. The measurement of behavioral health functioning relevant to the context of work requires the assessment of multiple dimensions of behavioral health functioning. Specifically, we identified a 4-factor model solution that represented key domains of work-related behavioral health functioning. These results guided the development and scale formation of a new SSA-BH instrument.

Validation of the Chinese version of the COVID-19 Phobia Scale among Chinese college students.

Background and objective: Different languages and versions of the COVID-19 Phobia Scale (C19P-S) have been developed and tested in several countries. Chinese college students are a large vulnerable group and are susceptible to psychological problems during the COVID-19 pandemic. However, no studies had yet examined the reliability and validity of the C19P-S in China among college students group. This study aims to evaluate the COVID-19-related phobia of Chinese college students and examine the reliability and validity of this scale. Methods: A total of 1689 Chinese college students participated in this study from April 27 to May 7, 2022. They finished the online questionnaire including demographic information and C19P-S. Cronbach's alpha and split-half reliability were used to examine the internal consistency of the scale. Confirmatory factor analysis was further used to examine the scale's construct validity. Convergence validity was also confirmed. Results: This scale in Chinese had high reliability and validity. The Cronbach's alpha and split-half reliability of the total scale were 0.960 and 0.935, respectively. The construct validity-related indicators of the total scale met the standards (RMSEA = 0.064, IFI = 0.907, TLI = 0.906, and CFI = 0.907). Regarding the subscales, the composite reliability (CR) and average variance extracted (AVE) also met the cutoff values (CR > 0.7 and AVE >0.5). Comparison between gender groups showed that total and subscale scores between male and female students differed significantly. Conclusion: The Chinese version of the C19P-S was appropriate for evaluating phobic symptoms among Chinese college students. Therefore, this tool could be used to evaluate the mental health of college students in the future.

Differential symptom cluster responses to repetitive transcranial magnetic stimulation treatment in depression.

Background: Repetitive transcranial magnetic stimulation (rTMS) can target specific neural circuits, which may allow for personalized treatment of depression. Treatment outcome is typically determined using sum scores from validated measurement scales; however, this may obscure differential improvements within distinct symptom domains. The objectives for this work were to determine: (1) whether a standard depression measure can be represented using a four symptom cluster model and (2) whether these symptom clusters had a differential response to rTMS treatment. Methods: Data were obtained from two multi-centre randomized controlled trials of rTMS delivered to the left dorsolateral prefrontal cortex (DLPFC) for participants with treatment-resistant depression (TRD) conducted in Canada (THREE-D [Conducted between Sept 2013, and Oct 2016] and CARTBIND [Conducted between Apr 2016 and Feb 2018]). The first objective used confirmatory factor analytic techniques, and the second objective used a linear mixed effects model. Trial Registration: NCT01887782, NCT02729792. Findings: In the total sample of 596 participants with TRD, we found a model consisting of four symptom clusters adequately fit the data. The primary analysis using the THREE-D treatment trial found that symptom clusters demonstrated a differential response to rTMS treatment (F(3,5984) = 31.92, p < 0.001). The anxiety symptom cluster was significantly less responsive to treatment than other symptom clusters (t(6001) = -8.02, p < 0.001). These findings were replicated using data from the CARTBIND trial. Interpretation: There are distinct symptom clusters experienced by individuals with TRD that have a differential response to rTMS. Future work will determine whether differing rTMS treatment targets have distinct patterns of symptom cluster responses with the eventual goal of personalizing rTMS protocols based on an individual's clinical presentation. Funding: Canadian Institutes of Health Research, Brain Canada.