Sufficient Covariate, Propensity Variable and Doubly Robust Estimation

Statistical causal inference from observational studies often requires adjustment for a possibly multi-dimensional variable, where dimension reduction is crucial. The propensity score, first introduced by Rosenbaum and Rubin, is a popular approach to such reduction. We address causal inference within Dawid's decision-theoretic framework, where it is essential to pay attention to sufficient covariates and their properties. We examine the role of a propensity variable in a normal linear model. We investigate both population-based and sample-based linear regressions, with adjustments for a multivariate covariate and for a propensity variable. In addition, we study the augmented inverse probability weighted estimator, involving a combination of a response model and a propensity model. In a linear regression with homoscedasticity, a propensity variable is proved to provide the same estimated causal effect as multivariate adjustment. An estimated propensity variable may, but need not, yield better precision than the true propensity variable. The augmented inverse probability weighted estimator is doubly robust and can improve precision if the propensity model is correctly specified

Robust correlation analyses: false positive and power validation using a new open source Matlab toolbox

Pearson’s correlation measures the strength of the association between two variables. The technique is, however, restricted to linear associations and is overly sensitive to outliers. Indeed, a single outlier can result in a highly inaccurate summary of the data. Yet, it remains the most commonly used measure of association in psychology research. Here we describe a free Matlab(R) based toolbox (http://sourceforge.net/projects/robustcorrtool/) that computes robust measures of association between two or more random variables: the percentage-bend correlation and skipped-correlations. After illustrating how to use the toolbox, we show that robust methods, where outliers are down weighted or removed and accounted for in significance testing, provide better estimates of the true association with accurate false positive control and without loss of power. The different correlation methods were tested with normal data and normal data contaminated with marginal or bivariate outliers. We report estimates of effect size, false positive rate and power, and advise on which technique to use depending on the data at hand

A single-level random-effects cross-lagged panel model for longitudinal mediation analysis

Cross-lagged panel models (CLPMs) are widely used to test mediation with longitudinal panel data. One major limitation of the CLPMs is that the model effects are assumed to be fixed across individuals. This assumption is likely to be violated (i.e., the model effects are random across individuals) in practice. When this happens, the CLPMs can potentially yield biased parameter estimates and misleading statistical inferences. This article proposes a model named a random-effects cross-lagged panel model (RE-CLPM) to account for random effects in CLPMs. Simulation studies show that the RE-CLPM outperforms the CLPM in recovering the mean indirect and direct effects in a longitudinal mediation analysis when random effects exist in the population. The performance of the RE-CLPM is robust to a certain degree, even when the random effects are not normally distributed. In addition, the RE-CLPM does not produce harmful results when the model effects are in fact fixed in the population. Implications of the simulation studies and potential directions for future research are discussed

Is Taking a Pill a Day Good for Health Expenditures? Evidence from a Cross Section Time Series Analysis of 19 OECD Countries from 1970 – 2000

This paper differs in two ways from previous comparative health system research. First, it focuses on the impact of pharmaceutical expenditures on total health expenditures as trends in pharmaceutical expenditures have been blamed of being a major driver of national health expenditures. In addition to pharmaceutical expenditures, other variables of interest are income, public financing, public delivery, ageing and urbanization. Second, the analysis includes a thorough sensitivity analysis on the proposed model using four samples (with and without the US, and imputed and not imputed data) to address the issue of robustness. Based on a typology of health care systems, trends of relevant explanatory variables are described using OECD Health Data 2003 data. Unlike any other of the variables, pharmaceutical expenditures show contradicting trends when measured as per capita pharmaceutical expenditures and pharmaceutical share of total health expenditures. Next, a regression analysis is performed on data from 1970 – 2000 for 19 OECD countries. Regression diagnostics indicated the absence of multicollinearity but the presence of heteroscedasticity and autocorrelation. Based on the Hausman test, a fixed effect model was chosen. As in all previous empirical research, per capita GDP turned out to be the most influential explanatory variable. While public financing of health care was always three out of four samples significantly inversely related to health expenditures, public delivery as a NHS dummy was always significantly positively related to the dependent variable. Unlike previous research, ageing is consistently and significantly related to higher total health expenditures and, so is urbanization. Finally, all samples show a highly negative relationship between share of pharmaceutical expenditures and health expenditures, suggesting support for the substitution theory.health care expenditure ; health care system ; health economics ; health policy ; comparative

Intraday forecasts of a volatility index: Functional time series methods with dynamic updating

As a forward-looking measure of future equity market volatility, the VIX index has gained immense popularity in recent years to become a key measure of risk for market analysts and academics. We consider discrete reported intraday VIX tick values as realisations of a collection of curves observed sequentially on equally spaced and dense grids over time and utilise functional data analysis techniques to produce one-day-ahead forecasts of these curves. The proposed method facilitates the investigation of dynamic changes in the index over very short time intervals as showcased using the 15-second high-frequency VIX index values. With the help of dynamic updating techniques, our point and interval forecasts are shown to enjoy improved accuracy over conventional time series models.Comment: 29 pages, 5 figures, To appear at the Annals of Operations Researc