Analyzing individual growth with clustered longitudinal data: A comparison between model-based and design-based multilevel approaches.

Using a multilevel latent growth curve modeling (LGCM) approach, this study examined longitudinal change in levels of physical fitness performance over time (i.e. four years) in young adolescents aged from 12–13 years. The sample consisted of 6622 students from 138 secondary schools in Singapore. Initial analyses found between-school variation on fitness test scores with intra-class correlations ranging from 0.02–0.19. Subsequent multilevel growth curve analyses revealed a quadratic trend of the longitudinal data across five stations of performance tests, with significant within-school student variability in change over time. The result of the multilevel LGCM showed that there were strong school effects on all of the physical fitness performances, in addition to inter- and intra-individual differences.

This contribution examines whether long-term utilization of extended education offerings in the German-speaking part of Switzerland has a positive effect on the development of school achievement (mathematics and reading achievement) and whether effects of family background on the development of school achievement can be reduced. For the analyses, multilevel latent growth curve models were calculated. When controlling for socioeconomic status and language spoken in the home, long-term utilization of extended education offerings had no effect on the development of school achievement. Further, there were no compensatory effects of long-term utilization of extended education offerings on the development of school achievement. This was the case for both students with German as a second language and students with low socioeconomic status.

The Growth Curve Model (GCM) is a Generalized Multivariate Analysis of Variance (GMANOVA) model especially useful in the analysis of longitudinal data, growth curves as well as other response curves. The model is a natural extension of the classical Multivariate Analysis of Variance (MANOVA) model and among other assumptions, relies on the assumption that the mean for each group can be represented as a polynomial of degree q. The assumption that the mean over time for all groups follows a polynomial of the same degree is not always satisfied, since individuals across the different groups may respond differently. An excellent scenario is when we have clustered longitudinal data, where the response over time can be represented by polynomials of different degrees. In such situations, the natural extension is to use the Extended Growth Curve Model (EGCM), where one can assume different shapes to represent different groups or clusters. In this paper, we formulate hypotheses motivated by real life scenarios involving clustered longitudinal data, and propose tests that are motivated by residuals in the EGCM. We then mathematically derive the tests and evaluate performances using simulations. We provide real data examples as illustrations.

Individual growth trajectories of psychological phenomena are often theorized to be nonlinear. Additionally, individuals’ measurement schedules might be unique. In a structural equation framework, latent growth curve model (LGM) applications typically have either (a) modeled nonlinearity assuming some degree of balance in measurement schedules, or (b) accommodated truly individually varying time points, assuming linear growth. This article describes how to fit 4 popular nonlinear LGMs (polynomial, shape-factor, piecewise, and structured latent curve) with truly individually varying time points, via a definition variable approach. The extension is straightforward for certain nonlinear LGMs (e.g., polynomial and structured latent curve) but in the case of shape-factor LGMs requires a reexpression of the model, and in the case of piecewise LGMs requires introduction of a general framework for imparting piecewise structure, along with tools for its automation. All 4 nonlinear LGMs with individually varying time scores are demonstrated using an empirical example on infant weight, and software syntax is provided. The discussion highlights some advantages of modeling nonlinear growth within structural equation versus multilevel frameworks, when time scores individually vary.

Arsenic toxicokinetic modeling and risk analysis: Progress, needs and applications

Introduction:There is accumulating cross-sectional evidence of decreased within-network resting-state functional connectivity (RSFC) and increased between-network RSFC when comparing older to younger samples, but results from longitudinal studies with healthy aging samples are sparse and less consistent. Some of the variability might occur due to differences in network definition and the fact that most atlases were trained on young adult samples. Applying these atlases to older cohorts implies the generalizability of network definitions to older individuals. However, because age is linked to a less segregated network architecture, this assumption might not be valid. To account for this, the Atlas55+ (A55) was recently published. The A55 was trained on a sample of people over the age of 55, making the network solutions suitable for studies on the aging process. Here, we want to compare the A55 to the popular Yeo-Krienen atlas to investigate whether and to what extent differences in network definition influence longitudinal changes of RSFC. For this purpose, the following networks were investigated: the occipital network (ON, “visual network”), the pericentral network (PN, “somatomotor network”), the medial frontoparietal network (M-FPN, “default network”), the lateral frontoparietal network (L-FPN, “control network”), and the midcingulo-insular network (M-CIN, “salience network”).Methods:Analyses were performed using longitudinal data from cognitively healthy older adults (N= 228, mean age at baseline = 70.8 years) with five measurement points over 7 years. To define the five networks, we used different variants of the two atlases. The spatial overlap of the networks was quantified using the dice similarity coefficient (DSC). RSFC trajectories within networks were estimated with latent growth curve models. Models of varying complexity were calculated, ranging from a linear model without interindividual variability in intercept and slope to a quadratic model with variability in intercept and slope. In addition, regressions were calculated in the models to explain the potential variance in the latent factors by baseline age, sex, and education. Finally, the regional homogeneity and the silhouette coefficient were computed, and the spin test and Wilcoxon-Mann-Whitney test were used to evaluate how well the atlases fit the data.Results:Median DSC across all comparisons was 0.67 (range: 0.20–0.93). The spatial overlap was higher for primary processing networks in comparison to higher-order networks and for intra-atlas comparisons versus inter-atlas comparisons. Three networks (ON, PN, M-FPN) showed convergent shapes of trajectories (linear vs. quadratic), whereas the other two networks (L-FPN, M-CIN) showed differences in change over time depending on the atlas used. The 95% confidence intervals of the estimated time and age effects overlapped in most cases, so that differences were mainly evident regarding thep-value. The evaluation of the fit of the atlases to the data indicates that the Yeo-Krienen atlas is more suitable for our dataset, although it was not trained on a sample of older individuals.Conclusions:The atlas choice affects the estimated average RSFC in some networks, which highlights the importance of this methodological decision for future studies and calls for careful interpretation of already published results. Ultimately, there is no standard about how to operationalize networks. However, future studies may use and compare multiple atlases to assess the impact of network definition on outcomes. Ideally, the fit of the atlases to the data should be assessed, and heuristics such as “similar age range” or “frequently used” should be avoided when selecting atlases. Further, the validity of the networks should be evaluated by computing their associations with behavioral measures.

General pedagogical knowledge (GPK) is regarded as a central component of the competence that teachers acquire during university teacher education. However, existing research on GPK typically uses only one or two measurement points to assess development and identify influencing factors. The present study draws on an annual survey of pre-service teachers’ GPK over 5 measurement points during the course of university teacher education (i.e. over the standard five-year study period). Latent growth curve models were used to assess knowledge development and explore potential influences. Knowledge development was best described as an increasing trend that flattens out over time. While students’ initial knowledge levels differed, their knowledge increase showed little interindividual variance. Initial knowledge level was related to the use of learning opportunities at the beginning of the study programme, but no significant association was identified between knowledge growth and increased learning opportunities over time. Moreover, initial knowledge level was predicted by the grade point average achieved in secondary school examinations but not by intrinsic motivation. Overall, the findings indicate that university teacher education effectively promotes GPK, with the entry phase being of particular significance.

PurposeTo investigate the influence of exercise intensity normalisation on intra- and inter-individual acute and adaptive responses to an interval training programme.MethodsNineteen cyclists were split in two groups differing (only) in how exercise intensity was normalised: 80% of the maximal work rate achieved in an incremental test (%dot{text{W}}max) vs. maximal sustainable work rate in a self-paced interval training session (%dot{text{W}}max-SP). Testing duplicates were conducted before and after an initial control phase, during the training intervention, and at the end, enabling the estimation of inter-individual variability in adaptive responses devoid of intra-individual variability.ResultsDue to premature exhaustion, the median training completion rate was 88.8% for the %dot{text{W}}max group, but 100% for the %dot{text{W}}max-SP the group. Ratings of perceived exertion and heart rates were not sensitive to how intensity was normalised, manifesting similar inter-individual variability, although intra-individual variability was minimised for the %dot{text{W}}max-SP group. Amongst six adaptive response variables, there was evidence of individual response for only maximal oxygen uptake (standard deviation: 0.027 L·min−1·week−1) and self-paced interval training performance (standard deviation: 1.451 W·week−1). However, inter-individual variability magnitudes were similar between groups. Average adaptive responses were also similar between groups across all variables.ConclusionsTo normalise completion rates of interval training, %dot{text{W}}max-SP should be used to prescribe relative intensity. However, the variability in adaptive responses to training may not reflect how exercise intensity is normalised, underlining the complexity of the exercise dose–adaptation relationship. True inter-individual variability in adaptive responses cannot always be identified when intra-individual variability is accounted for.Supplementary InformationThe online version contains supplementary material available at 10.1007/s00421-023-05340-y.

Both ad-hoc robust sandwich standard error estimators (design-based approach) and multilevel analysis (model-based approach) are commonly used for analyzing complex survey data with nonindependent observations. Although these 2 approaches perform equally well on analyzing complex survey data with equal between- and within-level model structures (B. O. Muthén & Satorra, 1995), the performances of these 2 approaches for analyzing multilevel data with unequal between- and within-level structures have not yet been systematically examined. In this study, we extended B. O. Muthén and Satorra's (1995) study by comparing these 2 approaches and an additional model-based maximum model for analyzing multilevel data considering number of clusters, cluster size, intraclass correlation, and the equality of different level structures. The simulation results showed the model-based maximum model generally performed well across conditions. This model is also recommended as an alternative for analyzing nonindependent survey data, especially when the information of the higher level model structure is not known.

Objective: The present study aimed to examine longitudinal trajectories of brooding and reflective rumination and to determine their parallel predictive effects on changes in suicidal ideation among high-risk adolescents using a latent growth curve modeling framework. Methods and Materials: A prospective four-wave longitudinal design was employed with a sample of 362 high-risk adolescents aged 13–17 years recruited from secondary schools and youth mental health services. Participants completed validated self-report measures of brooding and reflective rumination, suicidal ideation, and depressive symptoms at three-month intervals over a 12-month period. Measurement invariance across time was established prior to growth analyses. Unconditional latent growth curve models were first estimated separately for brooding, reflection, and suicidal ideation to assess intercepts and linear slopes. A parallel process latent growth model was subsequently specified to examine whether baseline levels and rates of change in rumination subtypes predicted trajectories of suicidal ideation while controlling for depressive symptoms and gender. Model fit was evaluated using CFI, TLI, RMSEA, and SRMR indices, and missing data were handled using full information maximum likelihood estimation. Findings: Results indicated significant positive linear growth in brooding and suicidal ideation over time, with substantial inter-individual variability in slopes. Reflective rumination demonstrated a stable mean trajectory but significant slope variance. In the parallel process model, the brooding intercept significantly predicted the suicidal ideation intercept (β = .41, p < .001), and the brooding slope significantly predicted growth in suicidal ideation (β = .38, p < .001). Reflective rumination did not significantly predict changes in suicidal ideation trajectories. Depressive symptoms remained a significant covariate of baseline suicidal ideation. Overall model fit indices indicated good structural fit. Conclusion: Findings identify brooding, but not reflective rumination, as a dynamic longitudinal risk mechanism contributing to escalating suicidal ideation among high-risk adolescents, underscoring the importance of targeting maladaptive rumination processes in prevention and intervention efforts.

The life cycle of the European eel (Anguilla anguilla) presents several distinctive features, such as high plasticity in body growth, marked sexual dimorphism, sex ratio strongly skewed in favor of females and sexual maturation largely dependent upon the size of individuals. A demographic model incorporating all these characteristics is derived on the basis of a multiple classification of individuals by age and size, and variability in individual growth is explicitly included. Existing theory for size-structured stocks is extended to include the dependence of sexual maturation on size, while natural mortality is age specific. Using 1989 population data from Comacchio lagoons (Italy), we estimate mortality and metamorphosis rate and abundance in each age- and size-class for both yellow and silver eels, crucial information for the management of the Comacchio fishery. The use of a nonparametric technique (bootstrapping) yields not only the moments, but also the distributions of these estimates. Validation of the model is performed on the data collected in 1990. The approach adopted is very flexible and different assumptions about survival, sexual maturation, and net selectivity can be easily incorporated in the model.

Understanding of fish growth, the spatial variability in individual growth, and the potential drivers of such variability is a fundamental component of many ecological investigations. However, sampling gears are always size-selective, and this selectivity can result in biased parameter estimates that can lead to, for example, biased stock assessments that use growth estimates. Using seven flathead catfish (Pylodictis olivaris) populations from across the USA as an example, we investigated to what degree the incorporation of gear selectivity in growth models reduces size-selective bias in the estimation of growth parameters during macroscale investigations of fish growth. We developed a series of simulation scenarios by combining different sampling methods to obtain fish samples and different gear selectivity assumptions to estimate parameters. Results showed that the efficacy of incorporating gear selectivity in growth models to reduce size-selective sampling bias during macroscale investigations depends on multiple factors, including (i) the size distribution of small and large fish in the sample (which is a function of sampling methods), and (ii) consistency of sampling methods across populations. Incorporation of gear selectivity may reduce bias when data are lacking for large fish and when sampling methods are inconsistent across populations. Demographics of the sampled populations and the growth parameter of interest can also affect the utility of directly incorporating gear selectivity into growth models. Because multiple factors can influence the efficacy of incorporating gear selectivity into growth models, the decision to do so likely needs to be made on a case-by-case basis. This study extends the existing gear selectivity research by focusing on macroscale fish growth investigations across multiple populations and provides guidance on how to handle gear selectivity assumptions during such investigations.

Age structure and growth of Stegastes fuscus were investigated during the present study. Individuals were collected monthly by divers using nets and spears in the reefs off Tamandare, Pernambuco, Brazil. Otoliths were removed from 346 individuals and sectioned transversally to determine individual age. Otolith sections showed a clear pattern of opaque and translucent bands. Opaque bands were counted and initially attributed to the age of individual fish. To determine the periodicity of band formation, a validation experiment was performed, in which individuals (n = 8) were injected with tetracycline (50 mg kg-1) and kept in the laboratory for periods of three months to one year. Results of the validation experiment showed that one opaque band is deposited per year. The age of individuals collected from January to December 1995 ranged between 0 and 15 years. Analysis of margins of monthly collected individuals suggested that opaque bands are deposited during the dry season, between September and March. Readings of tetracycline-marked otoliths corroborated these results. The length-at-age curve yielded a growth constant (K) of 0.19 y-1. The high variability of the length-at-age data indicated high variability in individual growth. Length–frequency data were also used to obtain growth parameters. The growth constant, as determined with these data was 0.6 y-1 and differed markedly from K values determined from length-at-age data. It was concluded that length-frequency data are not suitable to determine growth of this species. The present study showed that otoliths are a reliable structure for aging S. fuscus, which showed to be a relatively long-lived and slow-growing tropical reef species.

We examined growth in length of fluvial bull trout (Salvelinus confluentus) in the Walla Walla River Basin, Washington and Oregon. Our objectives were to quantify individual variability in growth; examine growth within and among years, life history forms, life stages and sexes; and estimate von Bertalanffy growth parameters. Individual variability was evaluated by modelling asymptotic length (L∞) and the growth coefficient (k) as random variables. All models were fit with Bayesian methods and were evaluated for fit by the deviance information criterion. By incorporating individual variability, population‐level estimates ofL∞andkappeared appropriate and estimated growth trajectories for specific bull trout fit individual observed patterns in growth. Growth trajectories and positive correlation between individual estimates ofL∞andksuggest that some individuals grow at a faster rate and reach a larger maximum size than other individuals and those differences are maintained throughout life. Selected models suggest that fluvial migrants have higher estimates ofL∞andkthan residents, but there were only slight differences in parameter estimates among migrants from two adjacent spawning populations in the Walla Walla River Basin, as well as between males and females. Growth rates increased for fluvial migrants after subadult emigration. Individual variability in growth is consistent with the life history diversity assumed essential for bull trout population persistence. Quantifying this variability is important for modelling population dynamics and viability to conserve this threatened species.

Levetiracetam is a broad-spectrum antiepileptic drug commonly used in intensive care units (ICUs). The objective of this study is to evaluate the adequacy of levetiracetam dosing in patients with normal or augmented renal clearance (ARC) admitted to the ICU by population modelling and simulation. A multicentre prospective study including twenty-seven critically ill patients with urinary creatinine clearance (CrCl) > 50 mL/min and treated with levetiracetam was developed. Levetiracetam plasma concentrations were best described by a two-compartment model. The parameter estimates and relative standard errors (%) were clearance (CL) 3.5 L/h (9%), central volume of distribution (V1) 20.7 L (18%), intercompartmental clearance 31.9 L/h (22%), and peripheral volume of distribution 33.5 L (13%). Interindividual variability estimates were, for the CL, 32.7% (21%) and, for V1, 56.1% (29%). The CrCl showed significant influence over CL. Simulations showed that the administration of at least 500 mg every 8 h or 1000 mg every 12 h are needed in patients with normal renal function. Higher doses (1500 or 2000 mg, every 8 h) are needed in patients with ARC. Critically ill patients with normal or ARC treated with levetiracetam could be at high risk of being underdosed.