Empirical Bayes Derivative Estimates

Abstract

A dynamic system is a set of interacting elements characterized by changes occurring over time. The estimation of derivatives is a mainstay for exploring dynamics of constructs, particularly when the dynamics are complicated or unknown. The presence of measurement error in many social science constructs frequently results in poor estimates of derivatives, as even modest proportions of measurement error can compound when estimating derivatives. Given the overlap in the specification of latent differential equation models and latent growth curve models, and the equivalence of latent growth curve models and mixed models under some conditions, derivatives could be estimated from estimates of random effects. This article proposes a new method for estimating derivatives based on calculating the Empirical Bayes estimates of derivatives from a mixed model. Two simulations compare four derivative estimation methods: Generalized Local Linear Approximation, Generalized Orthogonal Derivative Estimates, Functional Data Analysis, and the proposed Empirical Bayes Derivative Estimates. The simulations consider two data collection scenarios: short time series (≤10 observations) from many individuals or occasions, and long individual time series (25–500 observations). A substantive example visualizing the dynamics of intraindividual positive affect time series is also presented.     

Verbal and practical intelligence in general anxiety,obsessive compulsive and major depression disorders

IntroductionPrevious researches have shown that anxiety symptoms are negatively associated with measures of intelligence. However, recent findings indicate possible positive relationships between Generalized Anxiety Disorders (GAD) and intelligence. Also, Obsessive Compulsive Disorder (OCD) is associated with a moderate degree of underperformance on cognitive tests, including deficient processing. There are inconsistent results to present the relationship between Major Depression Disorder (MDD) and IQ. The present study has three main aims. The first aim of this study is to investigate the difference between IQ in individuals with GAD, OCD and major depressive disorder, and normal group. The second purpose is to perform a comparative study between the GAD, OCD and MDD groups on verbal and non-verbal intelligence. The third aim of this study is to examine the relationships between GAD, OCD and MDD as well as their underlying cognitive processes, including worry, rumination, and post-event processing, with verbal and non-verbal intelligence.ObjectiveThe present study is performed on four groups of participants including those with GAD, OCD, MDD and Healthy Volunteer (HV) group consisting of individuals without psychiatric disorders.MethodThe number of 50 healthy volunteers as the control group, 45 patients with GAD, 20 patients with OCD and 25 patients with MDD (n = 140) were selected as the case-referent groups. The present study was a cross-sectional type and the research was performed based on the causal-comparative method. Verbal and non-verbal intelligence was measured with the Wechsler Adult Intelligence Scale-3rd edition (WAIS-III). Rumination and post-event processing were measured by PSWQ, RRS-BR, and PEPQ, respectively.ResultsThe results indicate that Verbal Intelligence and Verbal Comprehension Index in GAD patients have significant differences in comparison to the OCD, MDD and control groups. While, the value of the Working Memory Index (WMI) in the normal group is higher than the value of the same index in the GAD, OCD and MDD groups. Also, the values of the Processing Speed Index (PSI) in normal and GAD groups are higher than the OCD and MDD groups. The worry, rumination, and post-event processing in patients with GAD are positively correlated with general and verbal intelligence. But, verbal and non-verbal intelligence had a negative correlation with worry, rumination and post-event processing in healthy volunteers.ConclusionInvestigation of the possible connections between intelligence and the cognitive processes underlying emotional disorders can provide therapeutic strategies for smart individuals who are at risk for GAD.