Hierarchical Model Fit Research Articles

Dynamic Fit Index Cutoffs for Hierarchical and Second-Order Factor Models

A recent review found that 11% of published factor models are hierarchical models with second-order factors. However, dedicated recommendations for evaluating hierarchical model fit have yet to emerge. Traditional benchmarks like RMSEA <0.06 or CFI >0.95 are often consulted, but they were never intended to generalize to hierarchical models. Through simulation, we show that traditional benchmarks perform poorly at identifying misspecification in hierarchical models. This corroborates previous studies showing that traditional benchmarks do not maintain optimal sensitivity to misspecification as model characteristics deviate from those used to derive the benchmarks. Instead, we propose a hierarchical extension to the dynamic fit index (DFI) framework, which automates custom simulations to derive cutoffs with optimal sensitivity for specific model characteristics. In simulations to evaluate performance, results showed that the hierarchical DFI extension routinely exceeded 95% classification accuracy and 90% sensitivity to misspecification whereas traditional benchmarks applied to hierarchical models rarely exceeded 50% classification accuracy and 20% sensitivity.

Improving estimates of phosphorus loads using hierarchical models

Estimates of nutrient loads are critical for managing the effects of nutrient pollution in receiving waters. An accurate calculation of load requires sub-daily, concurrent measurements of flow and nutrient concentrations. Continuous flow measurements are common, but nutrient concentrations are often measured infrequently, and so, statistical estimates of flow – concentration relationships are often used to infer nutrient concentration on unsampled days. Contributions of diffuse, nonpoint sources to flow – concentration relationships in neighboring sites may be similar, and methods are available to apportion in-stream concentrations to contributions from point and nonpoint sources. Combining a source apportionment model with a hierarchical statistical model may be a useful approach for leveraging information from more intensively sampled sites to improve estimates of relationships at more sparsely sampled sites. The approach is tested using daily measurements of total phosphorus and flow from eight rivers in Ohio, USA. Data from seven of the rivers are randomly subsampled to a single sample from each month, and a hierarchical model fit to estimate flow – concentration relationships for all sites. Hierarchical model estimates of phosphorus loads in subsampled sites were compared with three site-specific models: a linear flow – concentration relationship, a quadratic flow – concentration relationship with seasonal corrections, and Beale’s ratio method. The hierarchical model improved substantially on the precision of estimated total phosphorus loads at sparsely sampled sites, yielding an interquartile range of prediction errors of 22%. Simple linear load – concentration models were the next best performing method with an interquartile range of 33%. The average bias in hierarchical model predictions of phosphorus loads was 8%, whereas the smallest biases associated with the comparison methods were –10% for both the linear load – concentration model and Beale’s ratio. These results suggest that a hierarchical statistical model can be valuable for improving nutrient load estimates when data from a small number of intensively sites are available.

Predicting the growth of the amphibian chytrid fungus in varying temperature environments.

Environmental temperature is a crucial abiotic factor that influences the success of ectothermic organisms, including hosts and pathogens in disease systems. One example is the amphibian chytrid fungus, Batrachochytrium dendrobatidis (Bd), which has led to widespread amphibian population declines. Understanding its thermal ecology is essential to effectively predict outbreaks. Studies that examine the impact of temperature on hosts and pathogens often do so in controlled constant temperatures. Although varying temperature experiments are becoming increasingly common, it is unrealistic to test every temperature scenario. Thus, reliable methods that use constant temperature data to predict performance in varying temperatures are needed. In this study, we tested whether we could accurately predict Bd growth in three varying temperature regimes, using a Bayesian hierarchical model fit with constant temperature Bd growth data. We fit the Bayesian hierarchical model five times, each time changing the thermal performance curve (TPC) used to constrain the logistic growth rate to determine how TPCs influence the predictions. We then validated the model predictions using Bd growth data collected from the three tested varying temperature regimes. Although all TPCs overpredicted Bd growth in the varying temperature regimes, some functional forms performed better than others. Varying temperature impacts on disease systems are still not well understood and improving our understanding and methodologies to predict these effects could provide insights into disease systems and help conservation efforts.

A space–time statistical climate model for hurricane intensification in the North Atlantic basin

Abstract. Climate influences on hurricane intensification are investigated by averaging hourly intensification rates over the period 1975–2014 in 8° × 8° latitude–longitude grid cells. The statistical effects of hurricane intensity and sea-surface temperature (SST), along with the climatic effects of El Niño–Southern Oscillation (ENSO), the North Atlantic Oscillation (NAO) and the Madden–Julian Oscillation (MJO), are quantified using a Bayesian hierarchical model fit to the averaged data. As expected, stronger hurricanes tend to have higher intensification rates, especially over the warmest waters. Of the three climate variables considered, the NAO has the largest effect on intensification rates after controlling for intensity and SST. The model shows an average increase in intensification rates of 0.18 [0.06, 0.31] m s−1 h−1 (95 % credible interval) for every 1 standard deviation decrease in the NAO index. Weak trade winds associated with the negative phase of the NAO might result in less vertical wind shear and thus higher mean intensification rates.

Construct distinctiveness and variance composition of multi-dimensional instruments: Three short-form masculinity measures.

Focusing on a set of 3 multidimensional measures of conceptually related but different aspects of masculinity, we use factor analytic techniques to address 2 issues: (a) whether psychological constructs that are theoretically distinct but require fairly subtle discriminations by survey respondents can be accurately captured by self-report measures, and (b) how to better understand sources of variance in subscale and total scores developed from such measures. The specific measures investigated were the: (a) Male Role Norms Inventory-Short Form (MRNI-SF); (b) Conformity to Masculine Norms Inventory-46 (CMNI-46); and (c) Gender Role Conflict Scale-Short Form (GRCS-SF). Data (N = 444) were from community-dwelling and college men who responded to an online survey. EFA results demonstrated the discriminant validity of the 20 subscales comprising the 3 instruments, thus indicating that relatively subtle distinctions between norms, conformity, and conflict can be captured with self-report measures. CFA was used to compare 2 different methods of modeling a broad/general factor for each of the 3 instruments. For the CMNI-46 and MRNI-SF, a bifactor model fit the data significantly better than did a hierarchical factor model. In contrast, the hierarchical model fit better for the GRCS-SF. The discussion addresses implications of these specific findings for use of the measures in research studies, as well as broader implications for measurement development and assessment in other research domains of counseling psychology which also rely on multidimensional self-report instruments.

Bayesian Estimation of Age and Length at 50% Maturity

AbstractFish age and length at 50% maturity are used extensively in the management of exploited fish populations. These parameters are historically estimated using logistic regression models (e.g., frequentist inference) for individual year‐classes and often fail to converge or result in insignificant results when a small sample size is used. The sample‐size problem motivated us to evaluate whether a hierarchical logistic regression model fit using frequentist inference or Bayesian inference, could improve our ability to fit these models. Our objective was to compare Bayesian and frequentist inference for estimating age and length at 50% maturity to determine whether the models produced similar values. To make this evaluation, we used a long‐term data set of Yellow Perch Perca flavescens from southern Lake Michigan. Frequentist inference of the year‐class‐specific models resulted in significant results when sample size was sufficiently large, a result that occurred in 76% of the models. The hierarchical model produces estimates of age (or length) at 50% maturity for all year‐classes using both frequentist and Bayesian inference. However, Bayesian inference of the hierarchical model resulted in more precise parameter estimates and provided the complete posterior distribution in one seamless and easy approach, and the computation time was 78% to 83% faster. We suggest that a hierarchical model fit using Bayesian inference of age (or length) at 50% maturity is an improvement over frequentist interference methods by providing more information about the population of interest, particularly when sample sizes are limited.

Factor Structure of Decisional Balance and Temptations Scales for Smoking: Cross-Validation in Urban Female African-American Adolescents

The transtheoretical model is an influential theoretical model in health psychology, particularly in its application to smoking cessation research. Decisional Balance (DB) and Temptations are key constructs within this framework. This study examines the psychometric properties of the DB and Temptations scales for smoking in a predominantly African-American sample of urban adolescent girls. We used confirmatory factor analysis to compare the fit of previously published factor structures in smokers (n = 233) and nonsmokers (n = 598). External validity was tested by examining stages of change differences in the retained subscales. Results supported the internal and external validity of the DB scale for smokers and nonsmokers. Notably, previously published three-factor (Social Pros, Coping Pros, Cons) and four-factor (Cons split into "Aesthetic Cons" and "Health Cons") models fit equally well, with Cons subscales correlating highly. For Temptations, a previously published three-factor (Negative Affect, Social, Weight Control) hierarchical model fit well in nonsmokers. In smokers, previously published subscales were reliably measured, but their structural relationship remained unclear. Stage difference tests showed medium to large effect sizes of DB and Temptation subscales in smokers and nonsmokers. The use of DB was validated for both smokers and nonsmokers in this sample of primarily African-American adolescent females, where Cons can be combined or separated into "Aesthetic Cons" and "Health Cons" based on practical utility and preference. For Temptations, more research is needed but large stage differences in Temptations subscales underscore the importance of this concept in smoking acquisition and cessation.

Histograms based on the minimum description length principle

Histograms have been widely used for selectivity estimation in query optimization, as well as for fast approximate query answering in many OLAP, data mining, and data visualization applications. This paper presents a new family of histograms, the Hierarchical Model Fitting (HMF) histograms, based on the Minimum Description Length principle. Rather than having each bucket of a histogram described by the same type of model, the HMF histograms employ a local optimal model for each bucket. The improved effectiveness of the locally chosen models offsets more than the overhead of keeping track of the representation of each individual bucket. Through a set of experiments, we show that the HMF histograms are capable of providing more accurate approximations than previously proposed techniques for many real and synthetic data sets across a variety of query workloads.

A Spatiotemporal Model for Pollutant Concentrations

ABSTRACT Contamination of underground water tables can be characterized by measurements that are mixtures of short-term spiking, long-term decline, and steady-state variations in contaminant levels. Classical statistical models often fail to capture the changes in contaminant flow because they rely on fitting smooth spatial and temporal functions across the region, smooth functions that might not comprehensively characterize contaminant change. In this article, a more comprehensive approach is presented for modeling such processes. This approach uses a new class of spatiotemporal models that can characterize a broad range of environmental processes. It also effectively uses Bayesian hierarchical model fitting and a novel use of near neighbors to model contamination in an underground water table.

A Multidimensional Contingency Table Analysis of Parole Outcome

A major trend in the development of prediction in criminal justice has been toward increased statistical sophistication of methods. This study examines the utility of a new statistical method—log-linear analysis—as a means of predicting parole success relative to the Burgess method in both a construction and cross-validation sample. In addition, a replication study of the derived log- linear model was performed. The results suggest that the more sophisticated technique does not improve the ability to predict parole success beyond that achieved by the simpler method. Further, the hierarchical model emerging from the construction sample did not replicate in the validation sample. These results, when read in light of other studies, indicate that improvement in statistical technique may not be the best means of improving predictive effi ciency. The results also indicate that replication of hierarchical model fitting cannot be assumed, but rather must be studied empirically. The implications of these results are discussed for prediction research and theory testing.