Estimating causal effects from panel data with dynamic multivariate panel models.

Panel data are ubiquitous in scientific fields such as social sciences. Various modeling approaches have been presented for observational causal inference based on such data. Existing approaches typically impose restrictive assumptions on the data-generating process such as Gaussian responses or time-invariant effects, or they can only consider short-term causal effects. To surmount these restrictions, we present the dynamic multivariate panel model (DMPM) that supports time-varying, time-invariant, and individual-specific effects, multiple responses across a wide variety of distributions, and arbitrary dependency structures of lagged responses of any order. We formally demonstrate how DMPM facilitates causal inference within the structural causal modeling framework and we take a Bayesian approach for the estimation of the posterior distributions of the model parameters and causal effects of interest. We demonstrate the use of DMPM by applying the approach to both real and synthetic data.

Can Visualization Alleviate Dichotomous Thinking? Effects of Visual Representations on the Cliff Effect.

Common reporting styles for statistical results in scientific articles, such as p-values and confidence intervals (CI), have been reported to be prone to dichotomous interpretations, especially with respect to the null hypothesis significance testing framework. For example when the p-value is small enough or the CIs of the mean effects of a studied drug and a placebo are not overlapping, scientists tend to claim significant differences while often disregarding the magnitudes and absolute differences in the effect sizes. This type of reasoning has been shown to be potentially harmful to science. Techniques relying on the visual estimation of the strength of evidence have been recommended to reduce such dichotomous interpretations but their effectiveness has also been challenged. We ran two experiments on researchers with expertise in statistical analysis to compare several alternative representations of confidence intervals and used Bayesian multilevel models to estimate the effects of the representation styles on differences in researchers' subjective confidence in the results. We also asked the respondents' opinions and preferences in representation styles. Our results suggest that adding visual information to classic CI representation can decrease the tendency towards dichotomous interpretations - measured as the 'cliff effect': the sudden drop in confidence around p-value 0.05 - compared with classic CI visualization and textual representation of the CI with p-values. All data and analyses are publicly available at https://github.com/helske/statvis.

A nonlinear mixed model approach to predict energy expenditure from heart rate.

Objective.Heart rate (HR) monitoring provides a convenient and inexpensive way to predict energy expenditure (EE) during physical activity. However, there is a lot of variation among individuals in the EE-HR relationship, which should be taken into account in predictions. The objective is to develop a model that allows the prediction of EE based on HR as accurately as possible and allows an improvement of the prediction using calibration measurements from the target individual.Approach.We propose a nonlinear (logistic) mixed model for EE and HR measurements and an approach to calibrate the model for a new person who does not belong to the dataset used to estimate the model. The calibration utilizes the estimated model parameters and calibration measurements of HR and EE from the person in question. We compare the results of the logistic mixed model with a simpler linear mixed model for which the calibration is easier to perform.Main results.We show that the calibration is beneficial already with only one pair of measurements on HR and EE. This is an important benefit over an individual-level model fitting, which requires a larger number of measurements. Moreover, we present an algorithm for calculating the confidence and prediction intervals of the calibrated predictions. The analysis was based on up to 11 pairs of EE and HR measurements from each of 54 individuals of a heterogeneous group of people, who performed a maximal treadmill test.Significance.The proposed method allows accurate energy expenditure predictions based on only a few calibration measurements from a new individual without access to the original dataset, thus making the approach viable for example on wearable computers.

A Bayesian Reconstruction of a Historical Population in Finland, 1647-1850.

This article provides a novel method for estimating historical population development. We review the previous literature on historical population time-series estimates and propose a general outline to address the well-known methodological problems. We use a Bayesian hierarchical time-series model that allows us to integrate the parish-level data set and prior population information in a coherent manner. The procedure provides us with model-based posterior intervals for the final population estimates. We demonstrate its applicability by estimating the long-term development of Finland's population from 1647 onward and simultaneously place the country among the very few to have an annual population series of such length available.