Explore the vast range of titles available.

Individual-level longitudinal data on biological, behavioural, and social dimensions are becoming increasingly available. Typically, these data are analysed using mixed effects models, with the result summarised in terms of an average trajectory plus measures of the individual variations around this average. However, public health investigations would benefit from finer modelling of these individual variations which identify not just one average trajectory, but several typical trajectories. If evidence of heterogeneity in the development of these variables is found, the role played by temporally preceding (explanatory) variables as well as the potential impact of differential trajectories may have on later outcomes is often of interest. A wide choice of methods for uncovering typical trajectories and relating them to precursors and later outcomes exists. However, despite their increasing use, no practical overview of these methods targeted at epidemiological applications exists. Hence we provide: (a) a review of the three most commonly used methods for the identification of latent trajectories (growth mixture models, latent class growth analysis, and longitudinal latent class analysis); and (b) recommendations for the identification and interpretation of these trajectories and of their relationship with other variables. For illustration, we use longitudinal data on childhood body mass index and parental reports of fussy eating, collected in the Avon Longitudinal Study of Parents and Children.

ObjectivesLatent class trajectory modelling (LCTM) is a relatively new methodology in epidemiology to describe life-course exposures, which simplifies heterogeneous populations into homogeneous patterns or classes. However, for a given dataset, it is possible to derive scores of different models based on number of classes, model structure and trajectory property. Here, we rationalise a systematic framework to derive a ‘core’ favoured model.MethodsWe developed an eight-step framework: step 1: a scoping model; step 2: refining the number of classes; step 3: refining model structure (from fixed-effects through to a flexible random-effect specification); step 4: model adequacy assessment; step 5: graphical presentations; step 6: use of additional discrimination tools (‘degree of separation’; Elsensohn’s envelope of residual plots); step 7: clinical characterisation and plausibility; and step 8: sensitivity analysis. We illustrated these steps using data from the NIH-AARP cohort of repeated determinations of body mass index (BMI) at baseline (mean age: 62.5 years), and BMI derived by weight recall at ages 18, 35 and 50 years.ResultsFrom 288 993 participants, we derived a five-class model for each gender (men: 177 455; women: 111 538). From seven model structures, the favoured model was a proportional random quadratic structure (model F). Favourable properties were also noted for the unrestricted random quadratic structure (model G). However, class proportions varied considerably by model structure—concordance between models F and G were moderate (Cohen κ: men, 0.57; women, 0.65) but poor with other models. Model adequacy assessments, evaluations using discrimination tools, clinical plausibility and sensitivity analyses supported our model selection.ConclusionWe propose a framework to construct and select a ‘core’ LCTM, which will facilitate generalisability of results in future studies.

Statistical latent class models are widely used in social and psychological researches, yet it is often difficult to establish the identifiability of the model parameters. In this paper, we consider the identifiability issue of a family of restricted latent class models, where the restriction structures are needed to reflect pre-specified assumptions on the related assessment. We establish the identifiability results in the strict sense and specify which types of restriction structure would give the identifiability of the model parameters. The results not only guarantee the validity of many of the popularly used models, but also provide a guideline for the related experimental design, where in the current applications the design is usually experience based and identifiability is not guaranteed. Theoretically, we develop a new technique to establish the identifiability result, which may be extended to other restricted latent class models.

This article focuses on a family of restricted latent structure models with wide applications in psychological and educational assessment, where the model parameters are restricted via a latent structure matrix to reflect prespecified assumptions on the latent attributes. Such a latent matrix is often provided by experts and assumed to be correct upon construction, yet it may be subjective and misspecified. Recognizing this problem, researchers have been developing methods to estimate the matrix from data. However, the fundamental issue of the identifiability of the latent structure matrix has not been addressed until now. The first goal of this article is to establish identifiability conditions that ensure the estimability of the structure matrix. With the theoretical development, the second part of the article proposes a likelihood-based method to estimate the latent structure from the data. Simulation studies show that the proposed method outperforms the existing approaches. We further illustrate the method through a dataset in educational assessment. Supplementary materials for this article are available online.

Latent class models have wide applications in social and biological sciences. In many applications, prespecified restrictions are imposed on the parameter space of latent class models, through a design matrix, to reflect practitioners’ assumptions about how the observed responses depend on subjects’ latent traits. Though widely used in various fields, such restricted latent class models suffer from nonidentifiability due to their discreteness nature and complex structure of restrictions. This work addresses the fundamental identifiability issue of restricted latent class models by developing a general framework for strict and partial identifiability of the model parameters. Under correct model specification, the developed identifiability conditions only depend on the design matrix and are easily checkable, which provide useful practical guidelines for designing statistically valid diagnostic tests. Furthermore, the new theoretical framework is applied to establish, for the first time, identifiability of several designs from cognitive diagnosis applications.

[Display omitted] •Omnichannel deal prone segments use different channels to procure and use promotions.•Motivation, opportunity, and ability factors predict segment membership.•Omnichannel deal prone segments focus either on offline or online, but not on both.•Online and On-and-offline segments respond more to promotions than offline segments.•Managers can use results to target deals to the right segments in the right channels. Today's retail promotional environment is driven by channel proliferation, customer channel preferences, and managers’ efforts to create a unified “omnichannel” customer experience. This paper identifies the omnichannel deal prone segments that emerge in this environment, that is, segments that employ multiple channels to procure and use promotions. We describe these segments, measure the motivations, opportunities, and abilities (MOA) associated with segment membership, and quantify how these segments respond differently to promotions. We apply latent class cluster analysis to a database of over 1,000 respondents in three product categories. We find a rich array of omnichannel deal prone segments. Interestingly, 82% of consumers have bifurcated into online- or offline-focused deal prone segments. That is, most consumers use multiple channels to procure and use promotions, but they focus on either online or offline channels. Only seventeen percent of consumers strongly utilize both online and offline channels. We find that opportunity factors such as access to physical stores, and ability factors such as online shopping experience, explain this finding. We discuss how our results enable managers to target the right promotion designs to the right customers through the appropriate channels.

Pooling data from multiple cohorts and extending the time frame across childhood should minimize study-specific effects, enabling better characterization of childhood wheezing. To analyze wheezing patterns from early childhood to adolescence using combined data from five birth cohorts. We used latent class analysis to derive wheeze phenotypes among 7,719 participants from five birth cohorts with complete report of wheeze at five time periods. We tested the associations of derived phenotypes with late asthma outcomes and lung function, and investigated the uncertainty in phenotype assignment. We identified five phenotypes: never/infrequent wheeze (52.1%), early onset preschool remitting (23.9%), early onset midchildhood remitting (9%), persistent (7.9%), and late-onset wheeze (7.1%). Compared with the never/infrequent wheeze, all phenotypes had higher odds of asthma and lower forced expiratory volume in 1 second and forced expiratory volume in 1 second/forced vital capacity in adolescence. The association with asthma was strongest for persistent wheeze (adjusted odds ratio, 56.54; 95% confidence interval, 43.75-73.06). We observed considerable within-class heterogeneity at the individual level, with 913 (12%) children having low membership probability (<0.60) of any phenotype. Class membership certainty was highest in persistent and never/infrequent, and lowest in late-onset wheeze (with 51% of participants having membership probabilities <0.80). Individual wheezing patterns were particularly heterogeneous in late-onset wheeze, whereas many children assigned to early onset preschool remitting class reported wheezing at later time points. All wheeze phenotypes had significantly diminished lung function in school-age children, suggesting that the notion that early life episodic wheeze has a benign prognosis may not be true for a proportion of transient wheezers. We observed considerable within-phenotype heterogeneity in individual wheezing patterns.

The COVID-19 outbreak resulted in unprecedented restrictions on citizen’s freedom of movement as governments moved to institute lockdowns designed to reduce the spread of the virus. While most out-of-home leisure activities were prohibited, in England the lockdown rules allowed for restricted use of outdoor greenspace for the purposes of exercise and recreation. In this paper, we use data recorded by Google from location-enabled mobile devices coupled with a detailed recreation demand model to explore the welfare impacts of those constraints on leisure activities. Our analyses reveals evidence of large-scale substitution of leisure time towards recreation in available greenspaces. Indeed, despite the restrictions the economic value of greenspace to the citizens of England fell by only £150 million over lockdown. Examining the outcomes of counterfactual policies we find that the imposition of stricter lockdown rules would have reduced welfare from greenspace by £1.14 billion. In contrast, more relaxed lockdown rules would have delivered an aggregate increase in the economic value of greenspace equal to £1.47 billion.

Previous research has suggested that there is substantial heterogeneity in the developmental trajectories of attention-deficit/hyperactivity disorder (ADHD) symptoms. Sometimes, qualitative distinctions between trajectories with different ages of onset and/or patterns of remission are made; however, little is known about the predictors and broader clinical meaningfulness of these candidate 'developmental subtypes' of ADHD symptoms. We applied latent class growth analysis to data from the UK Millennium Cohort Study (MCS; N = 11 316; ages 3, 5, 7, 11 and 14) to evaluate whether developmental trajectories of ADHD symptoms differing in early life predictors could be identified. Our optimal model included six trajectory groups, labelled unaffected (34.9% of the sample), mildly affected (24.1%), subclinical remitting (12.8%), pre-school onset partially remitting (14.1%), developmentally increasing (7.6%) and pre-school onset persistent (6.4%). Factors such as gender, conduct problems, cognitive ability, maternal education, premature birth, peer problems and school readiness scores differentiated between specific ADHD symptom trajectories. Taken together, our findings provide preliminary evidence that distinguishing different trajectories of ADHD symptoms could be clinically informative.

In this paper, we propose a method by which the entrepreneurial ecosystem, if present, reveals itself in the data. We first follow the literature and define the entrepreneurial ecosystem as a multidimensional set of interacting factors that moderate the effect of entrepreneurial activity on economic growth. The quality of such an ecosystem, by its multidimensionality, is impossible to measure directly. But so defined, we argue that variation in entrepreneurial ecosystem quality should result in variation in the estimated marginal effect of entrepreneurial activity on economic growth. Testing for such variation is possible using a combination of a multilevel growth regression and latent class analysis. We motivate and validate our approach in simulated data before illustrating its applicability in a data set covering 107 European NUTS 1-2 regions across 16 EU member states. For this dataset, we cannot reject the hypothesis of a homogeneous contribution of entrepreneurship to regional growth. That is, in this dataset, we find no evidence of statistically significant heterogeneity in the estimated slope coefficients for entrepreneurial activity across regions. There are several possible explanations for this negative result. The two we deem most likely are first that the NUTS 1-2 level may not be disaggregated enough to coincide with the relevant boundaries of the entrepreneurial ecosystem. We suspect our method would reveal significant differences across smaller geographical units, but the data unfortunately do not yet allow us to empirically test this hypothesis in a multi-country regional analysis. The second possible explanation is that the growth rates from 2006 to 2014 coincided with the global financial and the European crisis, and during this time, the effect of entrepreneurship on (long-run average) growth overall has been obscured. Our simulations also suggested a third reason. If measurement error is large (in the order of 33 or 0.015% point annual GDP-growth), the effects may also have been obscured.