We present an idiographic approach to modeling dyadic interactions using differential equations. Using data representing daily affect ratings from romantic relationships, we examined several models conceptualizing different types of dyadic interactions. We fitted each model to each of the dyads and the resulting AICc values were used to classify the most likely configuration of interaction for each dyad. Additionally, the AICc from the different models were used in parameter averaging across models. Averaged parameters were used in models involving predictors of relationship dynamics, as indexed by these parameters, as well as models wherein the parameters predicted distal outcomes of the dyads such as relationship satisfaction and status. Results indicated that, within our sample, the most likely interaction style was that of independence, without evidence of emotional interrelations between the two individuals in the couple. Attachment-related avoidance and anxiety showed significant relations with model parameters, such that ideal levels of affect for males were negatively influenced by higher levels of avoidance from their partner while their own levels of anxiety had positive effects on their levels of dyadic coregulation. For females coregulation was negatively influenced by both time in the relationship and their partner’s level of avoidance. Analysis involving distal outcomes showed modest influences from the individual’s level of ideal affect.

A decade ago, a statistics-based method was introduced to count the number of atoms from annular dark-field scanning transmission electron microscopy (ADF STEM) images. In the past years, this method was successfully applied to nanocrystals of arbitrary shape, size, and composition (and its high accuracy and precision has been demonstrated). However, the counting results obtained from this statistical framework are so far presented without a visualization of the actual uncertainty about this estimate. In this paper, we present three approaches that can be used to represent counting results together with their statistical error, and discuss which approach is most suited for further use based on simulations and an experimental ADF STEM image.

When studying the Federal Open Market Committee’s (FOMC’s) interest rate rule, some authors, such as Gonzalez-Astudillo [(2018) Journal of Monetary, Credit, and Banking 50(1), 115–154.], find evidence for changes in inflation and output gap responses. Others, such as Sims and Zha [(2006) American Economic Review 96(1), 54–81.], only find evidence for a change in the variance of the interest rate rule. In this paper, I develop a new two-regime Markov-switching model that probabilistically performs variable selection and identification of parameter change for each variable in the model. I find substantial evidence that there have been changes in the FOMC’s response to the unemployment gap and in the volatility of the rule. When the FOMC responds strongly to the unemployment gap, I find a bimodal density for the inflation response coefficient. Despite the bimodal density, there is a low probability that there have been changes in the FOMC’s response to inflation.

We consider a model-averaged forecast-based estimate of the output gap to measure economic slack in 10 industrialized economies. Our measure takes changes in the long-run growth rate into account and, by addressing model uncertainty using equal weights on different forecast-based estimates, is robust to different assumptions about the underlying structure of the economy. For all 10 countries in the sample, we find that the estimated output gap has much larger negative movements during recessions than positive movements in expansions, suggesting business cycle asymmetry is an intrinsic characteristic of industrialized economies. Furthermore, the estimated output gap is always strongly negatively correlated with future output growth and unemployment and positively correlated with capacity utilization. It also implies a convex Phillips Curve in many cases. The model-averaged output gap is reliable in real time in the sense of being subject to relatively small revisions.

Objectives: Prior research has identified numerous genetic (including sex), education, health, and lifestyle factors that predict cognitive decline. Traditional model selection approaches (e.g., backward or stepwise selection) attempt to find one model that best fits the observed data, risking interpretations that only the selected predictors are important. In reality, several predictor combinations may fit similarly well but result in different conclusions (e.g., about size and significance of parameter estimates). In this study, we describe an alternative method, Information-Theoretic (IT) model averaging, and apply it to characterize a set of complex interactions in a longitudinal study on cognitive decline. Methods: Here, we used longitudinal cognitive data from 1256 late–middle aged adults from the Wisconsin Registry for Alzheimer’s Prevention study to examine the effects of sex, apolipoprotein E (APOE) ɛ4 allele (non-modifiable factors), and literacy achievement (modifiable) on cognitive decline. For each outcome, we applied IT model averaging to a set of models with different combinations of interactions among sex, APOE, literacy, and age. Results: For a list-learning test, model-averaged results showed better performance for women versus men, with faster decline among men; increased literacy was associated with better performance, particularly among men. APOE had less of an association with cognitive performance in this age range (∼40–70 years). Conclusions: These results illustrate the utility of the IT approach and point to literacy as a potential modifier of cognitive decline. Whether the protective effect of literacy is due to educational attainment or intrinsic verbal intellectual ability is the topic of ongoing work. (JINS, 2019, 25, 119–133)

We studied the ontogenetic growth of goat wethers (castrated male goats) of the Saanen and Swiss Alpine breeds based on a large range of intraspecific body mass (BM). The body parts and the chemical constituents of the empty body were described by the allometric function by using BM and the empty body mass (EBM) as the predictors for morphological traits and chemical composition, respectively. We fitted the allometric scaling function by applying the SAS NLMIXED procedure, but to evaluate assumptions regarding variances in morphological and compositional traits, we combined the scaling function with homoscedastic (MOD1), and the heteroscedastic exponential (MOD2) and power-of-the-mean (MOD3) variance functions. We also predicted the ontogenetic growth by using the traditional log-log transformation and back-transformed results into the arithmetic scale (MOD4). We obtained predictions from MOD4 in the arithmetic scale by a two-step process, and evaluated MOD1, MOD2 and MOD3 by a model selection framework, and compared MOD4 with MOD1, MOD2 and MOD3 based on goodness-of-fit measures. Based on information criteria for model selection, heterogeneous variance functions were more likely to describe 10 over 36 traits with a low level of model selection uncertainty. One trait was predicted by averaging the MOD1 and MOD2 variance functions; and nine traits were better described by averaging the MOD2 and MOD3 variance functions. The predictions for other 16 traits were averaged from MOD1, MOD2 and MOD3. However, MOD4 better described 11 traits according to the goodness-of-fit measures. Depending on the variable being analyzed, the body parts and the chemical amounts exhibited the three types of allometric behavior with respect to BM and EBM, that is, positive, negative and isometric ontogenetic growth. Reference BMs, that is, 20, 27, 35 and 45 kg, were used to compute the net protein and energy requirements based on the first derivative of the scaling function, and the results were presented in reference to the EBM and EBM0.75. Both the net protein and energy requirements scaled to EBM0.75 increased from 20 to 45 kg of BM.

Episode Treatment Groups (ETGs) classify related services into medically relevant and distinct units describing an episode of care. Proper model selection for those ETG-based costs is essential to adequately price and manage health insurance risks. The optimal claim cost model (or model probabilities) can vary depending on the disease. We compare four potential models (lognormal, gamma, log-skew-t and Lomax) using four different model selection methods (AIC and BIC weights, Random Forest feature classification and Bayesian model averaging) on 320 ETGs. Using the data from a major health insurer, which consists of more than 33 million observations from 9 million claimants, we compare the various methods on both speed and precision, and also examine the wide range of selected models for the different ETGs. Several case studies are provided for illustration. It is found that Random Forest feature selection is computationally efficient and sufficiently accurate, hence being preferred in this large data set. When feasible (on smaller data sets), Bayesian model averaging is preferred because of the posterior model probabilities.

In this paper we examine the claims reserving problem using Tweedie's compound Poisson model. We develop the maximum likelihood and Bayesian Markov chain Monte Carlo simulation approaches to fit the model and then compare the estimated models under different scenarios. The key point we demonstrate relates to the comparison of reserving quantities with and without model uncertainty incorporated into the prediction. We consider both the model selection problem and the model averaging solutions for the predicted reserves. As a part of this process we also consider the sub problem of variable selection to obtain a parsimonious representation of the model being fitted.