Many quantitative traits of economical importance are ordinal in natur
e. Although methods of mapping quantitative trait loci (QTLs) for cont
inuous quantitative characters are well developed, such methods for or
dinal characters are generally lacking. In this paper, we develop a me
thod based on the framework of a generalized linear model using four-w
ay cross populations. The method estimates and tests the average effec
ts of a gene substitution in the parents. All markers in the same link
age group are simultaneously used to infer the allelic transmission of
a putative QTL. General results of the method are demonstrated by a f
ew simulation experiments. We discuss extensions of the method to QTL
mapping in full-sib families.