Abstract
Generalized estimating equation (GEE) algorithm under a heterogeneous residual variance model is an extension of the iteratively reweighted least squares (IRLS) method for continuous traits to discrete traits. In contrast to mixture model-based expectation–maximization (EM) algorithm, the GEE algorithm can well detect quantitative trait locus (QTL), especially large effect QTLs located in large marker intervals in the manner of high computing speed. Based on a single QTL model, however, the GEE algorithm has very limited statistical power to detect multiple QTLs because of ignoring other linked QTLs. In this study, the fast least absolute shrinkage and selection operator (LASSO) is derived for generalized linear model (GLM) with all possible link functions. Under a heterogeneous residual variance model, the LASSO for GLM is used to iteratively estimate the non-zero genetic effects of those loci over entire genome. The iteratively reweighted LASSO is therefore extended to mapping QTL for discrete traits, such as ordinal, binary, and Poisson traits. The simulated and real data analyses are conducted to demonstrate the efficiency of the proposed method to simultaneously identify multiple QTLs for binary and Poisson traits as examples.
Highlights
Corresponding to continuous and discrete random variables in statistics, quantitative traits are classified into continuous and discrete traits in quantitative genetics
The earliest quantitative trait locus (QTL) mapping for continuous traits can be traced back to the interval mapping developed by Lander and Botstein [1], while the first group of people to map ordinal traits using the EM algorithm is credited to Hackett and Weller [2] and Xu and Atchley [3]
Two extensions are realized to map QTL for discrete traits: one is that of the Generalized estimating equation (GEE) algorithm under a heterogeneous residual variance model by Xu and Hu [21] for a single QTL model to multiple QTL model, and another is that of IRLASSO for the continuous normal traits [22] to discrete ones
Summary
Corresponding to continuous and discrete random variables in statistics, quantitative traits are classified into continuous and discrete traits in quantitative genetics. In contrast to discrete traits, continuous traits especially normally distributed ones are analyzed by taking advantage of the extensively developed inference methods available for linear models. Mapping methods for continuous quantitative traits are developed prior to discrete traits. Binary and categorical discrete traits are commonly observed that typically follow binomial and multinomial distributions. Binomial trait and multinomial trait can be regarded as the derivatives of binary and categorical or ordinal traits, defined by the proportions of the number of events happened among the total number of trials. The generalized linear model (GLM) becomes a natural choice for analyzing the discrete traits with the above mentioned distributions [4,5]. Some applications of GLM to mapping QTLs have been conducted for binary traits [3,6,7], ordinal traits [2,8] and Poisson traits [9,10]
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