Fitting latent growth models with small sample sizes and non-normal missing data

Shi, Dexin; DiStefano, Christine; Zheng, Xiaying; Liu, Ren; Jiang, Zhehan

doi:10.1177/0165025420979365

Cited by 47 publications

(29 citation statements)

References 42 publications

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“…While our results suggest that fixed effects are unbiased when residuals are nonnormally distributed, estimated random components should be reported cautiously, as the estimated individual differences in the intercept and slopes may be biased. This finding is consistent with previous studies (Maas & Hox, 2004;McNeish & Stapleton, 2016a;Raudenbush & Bryk, 2002;Shi et al, 2021;Searle et al, 2006). 3.…”

Section: # Sizesupporting

confidence: 94%

Effects of Compounded Nonnormality of Residuals in Hierarchical Linear Modeling

Man

Schumacker

Morell

et al. 2021

Educational and Psychological Measurement

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While hierarchical linear modeling is often used in social science research, the assumption of normally distributed residuals at the individual and cluster levels can be violated in empirical data. Previous studies have focused on the effects of nonnormality at either lower or higher level(s) separately. However, the violation of the normality assumption simultaneously across all levels could bias parameter estimates in unforeseen ways. This article aims to raise awareness of the drawbacks associated with compounded nonnormality residuals across levels when the number of clusters range from small to large. The effects of the breach of the normality assumption at both individual and cluster levels were explored. A simulation study was conducted to evaluate the relative bias and the root mean square of the model parameter estimates by manipulating the normality of the data. The results indicate that nonnormal residuals have a larger impact on the random effects than fixed effects, especially when the number of clusters and cluster size are small. In addition, for a simple random-effects structure, the use of restricted maximum likelihood estimation is recommended to improve parameter estimates when compounded residuals across levels show moderate nonnormality, with a combination of small number of clusters and a large cluster size.

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Section: # Sizesupporting

confidence: 94%

Effects of Compounded Nonnormality of Residuals in Hierarchical Linear Modeling

Man

Schumacker

Morell

et al. 2021

Educational and Psychological Measurement

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“…The estimation and statistical power of latent growth modeling increases with an increasing number of measurement occasions (Curran et al, 2010; Zhang & Wang, 2009), which may counterbalance the smaller sample size in our research to some degree (Hertzog et al, 2006). We also followed the recommendation of using the ML robust estimator (Shi et al, 2021) given the small sample size.…”

Section: Discussionmentioning

confidence: 99%

Is primary appraisal a mechanism of daily mindfulness at work?

Jamieson¹,

Tuckey²,

Li³

et al. 2022

Journal of Occupational Health Psychology

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In two studies, we examined primary appraisal as a potential mechanism of workplace mindfulness, grounded in the Transactional Model of Stress and Coping. In Study 1, multilevel structural equation modeling utilizing diary data from 58 employees across 5 working days showed that daily challenge appraisal mediated the positive relationship between mindfulness and high-activation positive affect, and daily threat appraisal mediated the negative relationship between mindfulness and high-activation negative affect. In Study 2, 69 employees participated in a randomized control trial comparing self-directed mindfulness training with a wait-list control. Latent growth curve modeling demonstrated that the intervention produced a greater increase in daily mindfulness relative to the control condition. In turn, the rate of change in daily mindfulness influenced the change rate of appraisal, and daily appraisal influenced affect, as expected. Together, these studies indicate one way in which mindfulness may help employees to thrive at work is by adaptively shaping the stressor appraisal process, and that connecting mindfulness training to primary appraisal may bolster the potential beneficial effects in the work context.

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“…It included a relatively small sample for LGCM (Kelley & Rausch, 2011 ) – a large sample size is typically recommended (e.g. >100) for latent modeling (Shi, DiStefano, Zheng, Liu, & Jiang, 2021 ) – which can introduce uncertainty into the models and conclusions. Thus, these findings must be considered exploratory and should be validated in larger studies.…”

Section: Discussionmentioning

confidence: 99%

Latent growth curve modeling of physical activity trajectories in a positive-psychology and motivational interviewing intervention for people with type 2 diabetes

Millstein

Golden

Healy

et al. 2022

Health Psychology and Behavioral Medicine

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Background: Physical activity is critical for preventing and treating Type 2 diabetes (T2D). It is important to identify different profiles of physical activity change among those participating in behavioral interventions to optimize intervention-person fit. Methods: This study analyzes longitudinal trajectories of change in moderate-to-vigorous physical activity (MVPA) in a positive psychology (PP) and motivational interviewing (MI) intervention for T2D, using latent growth curve modeling (LGCM). Objective measures of MVPA were collected using accelerometers at three time points: pre-intervention, immediately post-intervention, and eight weeks post-intervention. LGCM analyses identified subpopulations of participants who responded similarly to the intervention and examined if sociodemographic, medical and psychosocial characteristics were associated with MVPA trajectories. Results: Analyses included 47 participants with complete follow-ups: 49% male, 81% non-Hispanic white, average age 66.1 ( SD = 10.1). Overall, 36% of the participants increased MVPA while 57% did not. LGCM identified three profiles with distinct MVPA trajectories. Profile 1 (‘Started Low, No Change’; 65.8% of participants) with a starting mean of 4.54 min of MVPA/day and decreased by −3.36 min. Profile 2 (‘Moderate-High Start, Minimal Change,’ 27.4% of participants) and had a starting mean of 22.86 min/day of MVPA with an average increase of 1.03 min. Profile 3 (‘Moderate Start, Ended High’; 6.8% of participants), had a starting mean of 7.33 min MVPA/day, and increased by 28.4 min. Being male, younger, having fewer medical and psychiatric comorbidities were associated with increases in MVPA. Conclusions: This secondary analysis detected three distinct physical activity profiles during and after a PP-MI intervention. Future interventions can target individuals with characteristics that showed the greatest benefit and add additional supports to people in groups that did not increase physical activity as much. These findings show a need for targeted and sustained behavior change strategies during and after physical activity interventions. Trial registration: ClinicalTrials.gov; identifier: NCT03001999.

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Fitting latent growth models with small sample sizes and non-normal missing data

Cited by 47 publications

References 42 publications

Effects of Compounded Nonnormality of Residuals in Hierarchical Linear Modeling

Effects of Compounded Nonnormality of Residuals in Hierarchical Linear Modeling

Is primary appraisal a mechanism of daily mindfulness at work?

Latent growth curve modeling of physical activity trajectories in a positive-psychology and motivational interviewing intervention for people with type 2 diabetes

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