Not quite normal: Consequences of violating the assumption of normality in regression mixture models

Statistical power and false positive rates for interdependent outcomes are strongly influenced by test type: Implications for behavioral neuroscience

Statistical errors in preclinical science are a barrier to reproducibility and translation. For instance, linear models (e.g., ANOVA, linear regression) may be misapplied to data that violate assumptions. In behavioral neuroscience and psychopharmacology, linear models are frequently applied to interdependent or compositional data, which includes behavioral assessments where animals concurrently choose between chambers, objects, outcomes, or types of behavior (e.g., forced swim, novel object, place/social preference). The current study simulated behavioral data for a task with four interdependent choices (i.e., increased choice of a given outcome decreases others) using Monte Carlo methods. 16,000 datasets were simulated (1000 each of 4 effect sizes by 4 sample sizes) and statistical approaches evaluated for accuracy. Linear regression and linear mixed effects regression (LMER) with a single random intercept resulted in high false positives (>60%). Elevated false positives were attenuated in an LMER with random effects for all choice-levels and a binomial logistic mixed effects regression. However, these models were underpowered to reliably detect effects at common preclinical sample sizes. A Bayesian method using prior knowledge for control subjects increased power by up to 30%. These results were confirmed in a second simulation (8000 datasets). These data suggest that statistical analyses may often be misapplied in preclinical paradigms, with common linear methods increasing false positives, but potential alternatives lacking power. Ultimately, using informed priors may balance statistical requirements with ethical imperatives to minimize the number of animals used. These findings highlight the importance of considering statistical assumptions and limitations when designing research studies.

Common, uncommon, and novel applications of random forest in psychological research

Recent reform efforts have pushed toward a better understanding of the distinction between exploratory and confirmatory research, and appropriate use of each. As some utilize more exploratory tools, it may be tempting to employ multiple linear regression models. In this paper, we advocate for the use of random forest (RF) models. RF is able to obtain better predictive performance than traditional regression, while also inherently protecting against overfitting as well as detecting nonlinear effects and interactions among predictors. Given the advantages of RF compared to other statistical procedures, it is a tool commonly used within a plethora of industries, including stock trading, banking, pharmaceuticals, and patient healthcare planning. However, we find RF is used within the field of psychology comparatively less frequently. In the current paper, we advocate for RF as an important statistical tool within the context of behavioral and psychological research. In hopes of increasing the use of RF in the field of psychology, we provide information pertaining to the limitations one might confront in using RF and how to overcome such limitations. Moreover, we discuss various methods for how to optimally utilize RF with psychological data, such as nonparametric modeling, interaction and nonlinearity detection, variable selection, prediction and classification modeling, and assessing parameters of Monte Carlo simulations. Throughout, we illustrate the use of RF with visualization strategies, aimed to make RF models more comprehensible and intuitive.

George SM, Prinz R, Resnicow K. The Results of the Families Improving Together (FIT) for Weight Loss Randomized Trial in Overweight African American Adolescents

BACKGROUND

Few intervention studies have integrated cultural tailoring, parenting, behavioral, and motivational strategies to address African American adolescent weight loss.

PURPOSE

The Families Improving Together (FIT) for Weight Loss trial was a randomized group cohort study testing the efficacy of a cultural tailoring, positive parenting, and motivational intervention for weight loss in overweight African American adolescents (N = 241 adolescent/caregiver dyads).

METHODS

The trial tested an 8-week face-to-face group motivational plus family weight loss program (M + FWL) compared with a comprehensive health education control program. Participants were then rerandomized to an 8-week tailored or control online program to test the added effects of the online intervention on reducing body mass index and improving physical activity (moderate-to-vigorous physical activity [MVPA], light physical activity [LPA]), and diet.

RESULTS

There were no significant intervention effects for body mass index or diet. There was a significant effect of the group M + FWL intervention on parent LPA at 16 weeks (B = 33.017, SE = 13.115, p = .012). Parents in the group M + FWL intervention showed an increase in LPA, whereas parents in the comprehensive health education group showed a decrease in LPA. Secondary analyses using complier average causal effects showed a significant intervention effect at 16 weeks for parents on MVPA and a similar trend for adolescents.

CONCLUSIONS

While the intervention showed some impact on physical activity, additional strategies are needed to impact weight loss among overweight African American adolescents.

The Impact of Imposing Equality Constraints on Residual Variances Across Classes in Regression Mixture Models

The purpose of this study is to explore the impact of constraining class-specific residual variances to be equal by examining and comparing the parameter estimation of a free model and a constrained model under various conditions. A Monte Carlo simulation study was conducted under several conditions, including the number of predictors, class-specific intercepts, sample size, class-specific regression weights, and class proportion to evaluate the results for parameter estimation of the free model and the restricted model. The free model yielded a more accurate estimation than the restricted model for most of the conditions, but the accuracy of the free model estimation was impacted by the number of predictors, sample size, the disparity in the magnitude of class-specific slopes and intercepts, and class proportion. When equality constraints were imposed in residual variance discrepant conditions, the parameter estimates showed substantial inaccuracy for slopes, intercepts, and residual variances, especially for those in Class 2 (with a lower class-specific slope). When the residual variances were equal between the classes, the restricted model showed better performance under some conditions.

Assessing Differential Effects of Somatic Amplification to Positive Affect in Midlife and Late Adulthood-A Regression Mixture Approach

This study aims to provide an empirical demonstration of a novel method, regression mixture model, by examining differential effects of somatic amplification to positive affect and identifying the predictors that contribute to the differential effects. Data derived from the second wave of Midlife in the United States. The analytic sample consisted of 1,766 adults aged from 33 to 84 years. Regression mixture models were fitted using Mplus 7.4, and a two-step model-building approach was adopted. Three latent groups were identified consisting of a maladaptive (32.1%), a vulnerable (62.5%), and a resilient (5.4%) group. Six covariates (i.e., age, education level, positive relations with others, purpose in life, depressive symptoms, and physical health) significantly predicted the latent class membership in the regression mixture model. The study demonstrated the regression mixture model to be a flexible and efficient statistical tool in assessing individual differences in response to adversity and identifying resilience factors, which contributes to aging research.

Bovine Tuberculosis (Mycobacterium bovis) Outbreak Duration in Cattle Herds in Ireland: A Retrospective Observational Study

Bovine tuberculosis (bTB) outbreaks, caused by Mycobacterium bovis infection, are a costly animal health challenge. Understanding factors associated with the duration of outbreaks, known as breakdowns, could lead to better disease management policy development. We undertook a retrospective observational study (2012-2018) and employed Finite Mixture Models (FMM) to model the outcome parameter, and to investigate how factors were associated with duration for differing subpopulations identified. In addition to traditional risk factors (e.g., herd size, bTB history), we also explored farm geographic area, parcels/farm fragmentation, metrics of intensity via nitrogen loading, and whether herds were designated controlled beef finishing units (CBFU) as potential risk factors for increased duration. The final model fitted log-normal distributions, with two latent classes (k) which partitioned the population into a subpopulation around the central tendency of the distribution, and a second around the tails of the distribution. The latter subpopulation included longer breakdowns of policy interest. Increasing duration was positively associated with recent (<3 years) TB history and the number of reactors disclosed, (log) herd size, beef herd-type relative to other herd types, number of land parcels, area, being designated a CBFU ("feedlot") and having high annual inward cattle movements within the "tails" subpopulation. Breakdown length was negatively associated with the year of commencement of breakdown (i.e., a decreasing trend) and non-significantly with the organic nitrogen produced on the farm (N kg/hectare), a measure of stocking density. The latter finding may be due to confounding effects with herd size and area. Most variables contributed only moderately to explaining variation in breakdown duration, that is, they had moderate size effects on duration. Herd-size and CBFU had greater effect sizes on the outcome. The findings contribute to evidence-based policy formation in Ireland.

Mapping Dermatology Life Quality Index (DLQI) scores to EQ-5D utility scores using data of patients with atopic dermatitis from the National Health and Wellness Study

PURPOSE

To develop a mapping algorithm for generating EQ-5D-5-level (EQ-5D-5L) utility scores from the Dermatology Life Quality Index (DLQI) in patients with atopic dermatitis (AD).

METHODS

The algorithm was developed using data from 1232 patients from four countries participating in the National Health and Wellness Study. Spearman's rank correlation coefficient was used to evaluate the conceptual overlap between DLQI and EQ-5D-5L. Six mapping models (ordinary least squares [OLS], Tobit, three different two-part models, and a regression mixture model) were tested with different specifications to determine model performance and were ranked based on the sum of mean absolute error (MAE), and root mean squared error (RMSE).

RESULTS

The mean DLQI score was 7.23; mean EQ-5D-5L score was 0.78; and there were moderate negative correlations between DLQI and EQ-5D-5L scores (p = - 0.514). A regression mixture model with total DLQI, and age and sex as independent variables performed best for mapping DLQI to EQ-5D-5L (RMSE = 0.113; MAE = 0.079).

CONCLUSION

This was the first study to map DLQI to EQ-5D-5L exclusively in patients with AD. The regression mixture model with total DLQI, and age and sex as independent variables was the best performing model and accurately predicted EQ-5D-5L. The results of this mapping can be used to translate DLQI data from clinical studies to health state utility values in economic evaluations.

Finite Mixture Models with Student t Distributions: an Applied Example

The use of finite mixture modeling (FMM) to identify unobservable or latent groupings of individuals within a population has increased rapidly in applied prevention research. However, many prevention scientists are still unaware of the statistical assumptions underlying FMM. In particular, finite mixture models (FMMs) typically assume that the observed indicator variables are normally distributed within each latent subgroup (i.e., within-class normality). These assumptions are rarely met in applied psychological and prevention research, and violating these assumptions when fitting a FMM can lead to the identification of spurious subgroups and/or biased parameter estimates. Although new methods have been developed that relax the within-class normality assumption when fitting a FMM, prevention scientists continue to rely on FMM methods that assume within-class normality. The purpose of the current article is to introduce prevention researchers to a FMM method for heavy-tailed data: FMM with Student t distributions. We begin by reviewing the distributional assumptions that underlie FMM and the limitations of FMM with normal distributions. Next, we introduce FMM with Student t distributions, and show, step by step, the analytic and substantive results of fitting a FMM with normal and Student t distributions to data from a smoking-cessation trial. Finally, we extend the results of the applied example to draw conclusions about the use of FMM with Student t distributions in applied settings and to provide guidelines for researchers who wish to use these methods in their own research.

Assessing the Robustness of Mixture Models to Measurement Noninvariance

Recent work reframes direct effects of covariates on items in mixture models as differential item functioning (DIF) and shows that, when present in the data but omitted from the fitted latent class model, DIF can lead to overextraction of classes. However, less is known about the effects of DIF on model performance-including parameter bias, classification accuracy, and distortion of class-specific response profiles-once the correct number of classes is chosen. First, we replicate and extend prior findings relating DIF to class enumeration using a comprehensive simulation study. In a second simulation study using the same parameters, we show that, while the performance of LCA is robust to the misspecification of DIF effects, it is degraded when DIF is omitted entirely. Moreover, the robustness of LCA to omitted DIF differs widely based on the degree of class separation. Finally, simulation results are contextualized by an empirical example.

Geoacoustic inversion of the acoustic-pressure vertical phase gradient from a single vector sensor

A vector sensor can provide measurements of ocean acoustic fields in terms of the acoustic pressure and three-dimensional particle velocity, providing potentially highly-informative data for applications such as geoacoustic inversion. This paper applies nonlinear Bayesian inversion to vector sensor data to estimate seabed geoacoustic properties and uncertainties in South China Sea. Linear-frequency-modulated source transmissions, recorded as acoustic pressure and vertical particle velocity, are processed to estimate the vertical phase gradient of acoustic pressure at multiple frequencies as the inversion data. An advantage of this type of data is that it can be modeled without knowledge of the source spectrum, allowing inversion with an unknown source and a single sensor. Geoacoustic inversion of phase-gradient data is carried out and compared to inversion of the vertical acoustic impedance, another type of vector-sensor data, independent of the source spectrum, which has been considered previously. Model selection for the optimal number of seabed sediment layers is carried out using Bayesian information criterion, and parameter estimates, uncertainties, and correlations are calculated using delayed-rejection adaptive Metropolis-Hastings sampling. Results indicate a three-layer seabed model (including the semi-infinite basement), with properties in agreement with independent measurements including a high-resolution seismic profile and surficial sediment type from a core.

Repeated measures regression mixture models

Regression mixture models are one increasingly utilized approach for developing theories about and exploring the heterogeneity of effects. In this study we aimed to extend the current use of regression mixtures to a repeated regression mixture method when repeated measures, such as diary-type and experience-sampling method, data are available. We hypothesized that additional information borrowed from the repeated measures would improve the model performance, in terms of class enumeration and accuracy of the parameter estimates. We specifically compared three types of model specifications in regression mixtures: (a) traditional single-outcome model; (b) repeated measures models with three, five, and seven measures; and (c) a single-outcome model with the average of seven repeated measures. The results showed that the repeated measures regression mixture models substantially outperformed the traditional and average single-outcome models in class enumeration, with less bias in the parameter estimates. For sample size, whereas prior recommendations have suggested that regression mixtures require samples of well over 1,000 participants, even for classes at a large distance from each other (classes with regression weights of .20 vs. .70), the present repeated measures regression mixture models allow for samples as low as 200 participants with an increased number (i.e., seven) of repeated measures. We also demonstrate an application of the proposed repeated measures approach using data from the Sleep Research Project. Implications and limitations of the study are discussed.

The Effects of Sample Size on the Estimation of Regression Mixture Models

Regression mixture models are a statistical approach used for estimating heterogeneity in effects. This study investigates the impact of sample size on regression mixture's ability to produce "stable" results. Monte Carlo simulations and analysis of resamples from an application data set were used to illustrate the types of problems that may occur with small samples in real data sets. The results suggest that (a) when class separation is low, very large sample sizes may be needed to obtain stable results; (b) it may often be necessary to consider a preponderance of evidence in latent class enumeration; (c) regression mixtures with ordinal outcomes result in even more instability; and (d) with small samples, it is possible to obtain spurious results without any clear indication of there being a problem.

The Impact of Item Misspecification and Dichotomization on Class and Parameter Recovery in LCA of Count Data

Mixture analysis of count data has become increasingly popular among researchers of substance use, behavioral analysis, and program evaluation. However, this increase in popularity seems to have occurred along with adoption of some conventions in model specification based on arbitrary heuristics that may impact the validity of results. Findings from a systematic review of recent drug and alcohol publications suggested count variables are often dichotomized or misspecified as continuous normal indicators in mixture analysis. Prior research suggests that misspecifying skewed distributions of continuous indicators in mixture analysis introduces bias, though the consequences of this practice when applied to count indicators has not been studied. The present work describes results from a simulation study examining bias in mixture recovery when count indicators are dichotomized (median split; presence vs. absence), ordinalized, or the distribution is misspecified (continuous normal; incorrect count distribution). All distributional misspecifications and methods of categorizing resulted in greater bias in parameter estimates and recovery of class membership relative to specifying the true distribution, though dichotomization appeared to improve class enumeration accuracy relative to all other specifications. Overall, results demonstrate the importance of accurately modeling count indicators in mixture analysis, as misspecification and categorizing data can distort study outcomes.

A DIAGNOSTIC TOOL FOR CHECKING ASSUMPTIONS OF REGRESSION MIXTURE MODELS

Regression mixture models are becoming more widely used in applied research. It has been recognized that these models are quite sensitive to underlying assumptions, yet many of these assumptions are not directly testable. We discuss a diagnostic tool based on reconstructed residuals that can help uncover violations of model assumptions. These residuals are found by using the posterior probability of class membership to assign, based on a multinomial distribution, a class to each observation. Standard residual checks can be applied to these posterior draw residuals to explore violations of the model assumptions. We present several illustrations of the diagnostic tool.

An evaluation of the bootstrap for model validation in mixture models

Bootstrapping has been used as a diagnostic tool for validating model results for a wide array of statistical models. Here we evaluate the use of the non-parametric bootstrap for model validation in mixture models. We show that the bootstrap is problematic for validating the results of class enumeration and demonstrating the stability of parameter estimates in both finite mixture and regression mixture models. In only 44% of simulations did bootstrapping detect the correct number of classes in at least 90% of the bootstrap samples for a finite mixture model without any model violations. For regression mixture models and cases with violated model assumptions, the performance was even worse. Consequently, we cannot recommend the non-parametric bootstrap for validating mixture models. The cause of the problem is that when resampling is used influential individual observations have a high likelihood of being sampled many times. The presence of multiple replications of even moderately extreme observations is shown to lead to additional latent classes being extracted. To verify that these replications cause the problems we show that leave-k-out cross-validation where sub-samples taken without replacement does not suffer from the same problem.

An Empirical Assessment of the Sensitivity of Mixture Models to Changes in Measurement

The current study explored the extent to which variations in self-report measures across studies can produce differences in the results obtained from mixture models. Data (N = 854) come from a laboratory analogue study of methods for creating commensurate scores of alcohol- and substance-use-related constructs when items differ systematically across participants for any given measure. Items were manipulated according to four conditions, corresponding to increasing levels of alteration to item stems, response options, or both. In Study 1, results from latent class analyses (LCA) of alcohol consequences were compared across the four conditions, revealing differences in class enumeration and configuration. In Study 2, results from factor mixture models (FMM) of alcohol expectancies were compared across two of the conditions, revealing differences in patterns and magnitude of the factor loadings and thresholds. The results suggest that even subtle differences in measurement can have substantively meaningful effects on mixture model results.

Impact of an equality constraint on the class-specific residual variances in regression mixtures: A Monte Carlo simulation study

Regression mixture models are a novel approach to modeling the heterogeneous effects of predictors on an outcome. In the model-building process, often residual variances are disregarded and simplifying assumptions are made without thorough examination of the consequences. In this simulation study, we investigated the impact of an equality constraint on the residual variances across latent classes. We examined the consequences of constraining the residual variances on class enumeration (finding the true number of latent classes) and on the parameter estimates, under a number of different simulation conditions meant to reflect the types of heterogeneity likely to exist in applied analyses. The results showed that bias in class enumeration increased as the difference in residual variances between the classes increased. Also, an inappropriate equality constraint on the residual variances greatly impacted on the estimated class sizes and showed the potential to greatly affect the parameter estimates in each class. These results suggest that it is important to make assumptions about residual variances with care and to carefully report what assumptions are made.

A Note on the Use of Mixture Models for Individual Prediction

Mixture models capture heterogeneity in data by decomposing the population into latent subgroups, each of which is governed by its own subgroup-specific set of parameters. Despite the flexibility and widespread use of these models, most applications have focused solely on making inferences for whole or sub-populations, rather than individual cases. The current article presents a general framework for computing marginal and conditional predicted values for individuals using mixture model results. These predicted values can be used to characterize covariate effects, examine the fit of the model for specific individuals, or forecast future observations from previous ones. Two empirical examples are provided to demonstrate the usefulness of individual predicted values in applications of mixture models. The first example examines the relative timing of initiation of substance use using a multiple event process survival mixture model whereas the second example evaluates changes in depressive symptoms over adolescence using a growth mixture model.

Modeling predictors of latent classes in regression mixture models

The purpose of the current study is to provide guidance on a process for including latent class predictors in regression mixture models. We first examine the performance of current practice for using the 1-step and 3-step approaches where the direct covariate effect on the outcome is omitted. None of the approaches show adequate estimates of model parameters. Given that the step-1 of the three-step approach shows adequate results in class enumeration, we suggest using an alternative approach: 1) decide the number of latent classes without predictors of latent classes and 2) bring the latent class predictors into the model with the inclusion of hypothesized direct covariates effects. Our simulations show that this approach leads to good estimates for all model parameters. The proposed approach is demonstrated by using empirical data to examine the differential effects of family resources on students' academic achievement outcome. Implications of the study are discussed.

Heterogeneity in the Relationship of Substance Use to Risky Sexual Behavior Among Justice-Involved Youth: A Regression Mixture Modeling Approach

Justice-involved adolescents engage in high levels of risky sexual behavior and substance use, and understanding potential relationships among these constructs is important for effective HIV/STI prevention. A regression mixture modeling approach was used to determine whether subgroups could be identified based on the regression of two indicators of sexual risk (condom use and frequency of intercourse) on three measures of substance use (alcohol, marijuana and hard drugs). Three classes were observed among n = 596 adolescents on probation: none of the substances predicted outcomes for approximately 18 % of the sample; alcohol and marijuana use were predictive for approximately 59 % of the sample, and marijuana use and hard drug use were predictive in approximately 23 % of the sample. Demographic, individual difference, and additional sexual and substance use risk variables were examined in relation to class membership. Findings are discussed in terms of understanding profiles of risk behavior among at-risk youth.

Regression Mixture Models: Does Modeling the Covariance Between Independent Variables and Latent Classes Improve the Results?

Regression mixture models are increasingly used as an exploratory approach to identify heterogeneity in the effects of a predictor on an outcome. In this simulation study, we tested the effects of violating an implicit assumption often made in these models; that is, independent variables in the model are not directly related to latent classes. Results indicate that the major risk of failing to model the relationship between predictor and latent class was an increase in the probability of selecting additional latent classes and biased class proportions. In addition, we tested whether regression mixture models can detect a piecewise relationship between a predictor and outcome. Results suggest that these models are able to detect piecewise relations but only when the relationship between the latent class and the predictor is included in model estimation. We illustrate the implications of making this assumption through a reanalysis of applied data examining heterogeneity in the effects of family resources on academic achievement. We compare previous results (which assumed no relation between independent variables and latent class) to the model where this assumption is lifted. Implications and analytic suggestions for conducting regression mixture based on these findings are noted.

Evaluating differential effects using regression interactions and regression mixture models

Research increasingly emphasizes understanding differential effects. This paper focuses on understanding regression mixture models, a relatively new statistical methods for assessing differential effects by comparing results to using an interactive term in linear regression. The research questions which each model answers, their formulation, and their assumptions are compared using Monte Carlo simulations and real data analysis. The capabilities of regression mixture models are described and specific issues to be addressed when conducting regression mixtures are proposed. The paper aims to clarify the role that regression mixtures can take in the estimation of differential effects and increase awareness of the benefits and potential pitfalls of this approach. Regression mixture models are shown to be a potentially effective exploratory method for finding differential effects when these effects can be defined by a small number of classes of respondents who share a typical relationship between a predictor and an outcome. It is also shown that the comparison between regression mixture models and interactions becomes substantially more complex as the number of classes increases. It is argued that regression interactions are well suited for direct tests of specific hypotheses about differential effects and regression mixtures provide a useful approach for exploring effect heterogeneity given adequate samples and study design.

Challenges in modelling the random structure correctly in growth mixture models and the impact this has on model mixtures

Lifecourse trajectories of clinical or anthropological attributes are useful for identifying how our early-life experiences influence later-life morbidity and mortality. Researchers often use growth mixture models (GMMs) to estimate such phenomena. It is common to place constrains on the random part of the GMM to improve parsimony or to aid convergence, but this can lead to an autoregressive structure that distorts the nature of the mixtures and subsequent model interpretation. This is especially true if changes in the outcome within individuals are gradual compared with the magnitude of differences between individuals. This is not widely appreciated, nor is its impact well understood. Using repeat measures of body mass index (BMI) for 1528 US adolescents, we estimated GMMs that required variance-covariance constraints to attain convergence. We contrasted constrained models with and without an autocorrelation structure to assess the impact this had on the ideal number of latent classes, their size and composition. We also contrasted model options using simulations. When the GMM variance-covariance structure was constrained, a within-class autocorrelation structure emerged. When not modelled explicitly, this led to poorer model fit and models that differed substantially in the ideal number of latent classes, as well as class size and composition. Failure to carefully consider the random structure of data within a GMM framework may lead to erroneous model inferences, especially for outcomes with greater within-person than between-person homogeneity, such as BMI. It is crucial to reflect on the underlying data generation processes when building such models.

Finite Mixtures for Simultaneously Modelling Differential Effects and Non-Normal Distributions

Regression mixture models have been increasingly applied in the social and behavioral sciences as a method for identifying differential effects of predictors on outcomes. While the typical specification of this approach is sensitive to violations of distributional assumptions, alternative methods for capturing the number of differential effects have been shown to be robust. Yet, there is still a need to better describe differential effects that exist when using regression mixture models. The current study tests a new approach that uses sets of classes (called differential effects sets) to simultaneously model differential effects and account for non-normal error distributions. Monte Carlo simulations are used to examine the performance of the approach. The number of classes needed to represent departures from normality is shown to be dependent on the degree of skew. The use of differential effects sets reduced bias in parameter estimates. Applied analyses demonstrated the implementation of the approach for describing differential effects of parental health problems on adolescent body mass index using differential effects sets approach. Findings support the usefulness of the approach which overcomes the limitations of previous approaches for handling non-normal errors.

Differential Effects of Parental Controls on Adolescent Substance Use: For Whom Is the Family Most Important?

OBJECTIVE

Social control theory assumes that the ability of social constraints to deter juvenile delinquency will be invariant across individuals. This paper tests this hypothesis and examines the degree to which there are differential effects of parental controls on adolescent substance use.

METHODS

Analyses are based on self-reported data from 7,349 10th-grade students and rely on regression mixture models to identify latent classes of individuals who may vary in the effects of parental controls on drug use.

RESULTS

All parental controls were significantly related to adolescent drug use, with higher levels of control associated with less drug use. The effects of instrumental parental controls (e.g., parental management strategies) on drug use were shown to vary across individuals, while expressive controls (e.g., parent/child attachment) had uniform effects in reducing drug use. Specifically, poor family management and more favorable parental attitudes regarding children's drug use and delinquency had stronger effects on drug use for students who reported greater attachment to their neighborhoods, less acceptance of adolescent drug use by neighborhood residents, and fewer delinquent peers, compared to those with greater community and peer risk exposure. Parental influences were also stronger for Caucasian students versus those from other racial/ethnic groups, but no differences in effects were found based on students' gender or commitment to school.

CONCLUSIONS

The findings demonstrate support for social control theory, and also help to refine and add precision to this perspective by identifying groups of individuals for whom parental controls are most influential. Further, they offer an innovative methodology that can be applied to any criminological theory to examine the complex forces that result in illegal behavior.

Using regression mixture models with non-normal data: Examining an ordered polytomous approach

Mild to moderate skew in errors can substantially impact regression mixture model results; one approach for overcoming this includes transforming the outcome into an ordered categorical variable and using a polytomous regression mixture model. This is effective for retaining differential effects in the population; however, bias in parameter estimates and model fit warrant further examination of this approach at higher levels of skew. The current study used Monte Carlo simulations; three thousand observations were drawn from each of two subpopulations differing in the effect of X on Y. Five hundred simulations were performed in each of the ten scenarios varying in levels of skew in one or both classes. Model comparison criteria supported the accurate two class model, preserving the differential effects, while parameter estimates were notably biased. The appropriate number of effects can be captured with this approach but we suggest caution when interpreting the magnitude of the effects.