Quantile regression: another take on multivariate data

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Presenter:  Dr Murthy Mittinty, Research Fellow – Biostatistician, The University of Adelaide

Date: Aug 18, 2015

Time: 10:30am to 11:30am

Contact person:  Katrina Britnell, Partnerships Coordinator, NI
T: 08 8946 6838
E: katrina.britnell@cdu.edu.au

Location:  Yellow Building 1, Level 2, Room 48 (Savanna Room), Northern Institute, Casuarina Campus, Charles Darwin University

Target audience:  Open To the Public Seminar - All Welcome

Abstract:  When describing a single random variable we use a variety of measures such as mean, variance, 5th percentile, 25th percentile, 50th percentile, 75th percentiles, inter quartile range, simple range (min and max), and skewness. Even when plotting the Univariate graphs we use a variety of plots such as histograms, boxplot and tree plot. However, when it comes to analysing bivariate and multivariate data we tend to limit ourselves to a single technique: mean based analysis. 

Ordinary least square (OLS) regression, which allows estimating the conditional average effect, is a common method for understanding bivariate and multivariate associations. This method of analysis has dominated the data analysis scene for more than three centuries for its simplicity, ease of computational manipulability and interpretability. The focus was on averages as it was hard enough to obtain good estimates of average effects in the dark ages before computation. Further, as pointed out by Tukey, commercial statistical software as it existed was not set up to be modified, even though it often did not answer the research question of interest,.

Estimating mean and variance or just means are sufficient when the distribution of the variable of interest is either normal or binary or Poisson. When distributions are skewed, transforming data might help achieve normality and the use of OLS might result in a good fit, however the interpretations can be outlandish. Moreover, when distributions are skewed, bimodal, or heavy tailed, estimation of mean alone of bivariate/multivariate associations gives an incomplete picture about the variable.

With this understanding, this presentation introduces an alternative to the OLS regressions called Quantile Regression. Unlike OLS this method does not require strict assumptions of normality and it allows analysing the distribution of the variable of interest, in its entirety. Quantile regressions are best used for analysing skewed and heavy tailed data that are common in epidemiological and medical data. I will also detail mechanics of quantile regression in the presentation.

About Dr Mittinty:  Murthy N Mittinty is an accredited statistician; his PhD is in mathematical statistics from University of Canterbury, New Zealand. He has used statistical methods for analysing research questions in the areas of water, meteorology, bio-security and health surveys. His interests are in the analysis of longitudinal studies, statistical data of missing data, causal analysis, and information geometry. Apart from statistics, Murthy has an interest in photography, philosophy and logic.   Read online profile.

RSVP       by Monday 17 August via thenortherninstitute@cdu.edu.au

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