Quantile Regression in the Study of Developmental Sciences

Abstract

Linear regression analysis is one of the most common techniques applied in developmental research, but only allows for an estimate of the average relations between the predictor(s) and the outcome. This study describes quantile regression, which provides estimates of the relations between the predictor(s) and outcome, but across multiple points of the outcome’s distribution. Using data from the High School and Beyond and U.S. Sustained Effects Study databases, quantile regression is demonstrated and contrasted with linear regression when considering models with: (a) one continuous predictor, (b) one dichotomous predictor, (c) a continuous and a dichotomous predictor, and (d) a longitudinal application. Results from each example exhibited the differential inferences which may be drawn using linear or quantile regression.

Improving the reliability of student scores from speeded assessments: an illustration of conditional item response theory using a computer-administered measure of vocabulary

“…Conversely, items with short average response times, such as items 19 and 20, presented with standard deviations which illustrates less variability in the average response ( SD = 8.96 and 6.55, respectively). In order to more fully explore this relation, quantile regression (Koenker & Bassett, 1978; Petscher & Logan, 2014; Petscher, Logan, & Zhou, 2013) via the quantreg package (Koenker, 2013) in R (2013) was used to test if the association between average response time and the variance in response time was conditional on the average response time. At the .20 quantile (or approximately 20th percentile) of mean response time, the correlation between response time and variance in response time was r (1) = .58, p = .02, compared with the .25 quantile [ r (1) = .65, p = .004], the .75 quantile [ r (1) = .88, p < .001], and the .80 quantile [ r (1) = .87, p < .001].…”

The research impact of school psychology faculty

“…Quantile regression tries to minimize the sum of the absolute residuals and makes no assumptions about the distribution form of variables (Petscher & Logan, 2014). In its most basic form, quantile regression estimates the median of the dependent variable conditional on the values of the independent variables.…”

“…Uniquely, quantile regression allows for the estimation of the relationship between dependent and independent variables at multiple locations of the independent variable. Analyses for this study were conducted with the simultaneous-quantile regression routine in Stata to estimate the 25th, 50th, and 75th percentile locations and standard errors computed with 100 bootstrap replications (Petscher & Logan, 2014). Sample sizes were too small to allow convergence on precise and stable estimates of more extreme locations (Koenker & D'Orey, 1987).…”

A Quantile Regression Approach to Understanding the Relations Among Morphological Awareness, Vocabulary, and Reading Comprehension in Adult Basic Education Students

“…It is important to note that quantile regression utilizes an asymmetric weighting system of data points and therefore, all data points are “weighted” based upon their distance from the researcher-specified quantile for that estimation. Consequently, quantile regression is not synonymous with fitting a separate OLS regression line at each quantile (Petscher & Logan, 2014; Petscher et al, 2013). …”