Goldgar introduced a novel marker-based method for partitioning the variation of a quantitative trait into specific chromosomal regions. Unlike traditional linkage mapping methods, Goldgar's method does not require the estimation of statistical quantities characterizing each locus thought to influence the trait under scrutiny (e.g., allele frequencies, penetrances, etc.). Goldgar's method is thus more flexible and less model dependent than many traditional marker-based genetic analysis techniques. Unfortunately, however, many of the properties of Goldgar's method have not been investigated. In this paper, the utility of an extended version of Goldgar's approach is studied in settings in which sibships are taken as the sampling unit of interest. The extensions discussed resolve around the incorporation of a wider variety of effects and factors into Goldgar's basic model. Analytic studies pertaining to power, sample-size requirements, and estimation procedures for the proposed extended version of Goldgar's method are described. Hypothesis-testing strategies are also discussed. The results of the analytic studies indicate that, although an extended sib-pair version of Goldgar's variance-partitioning approach to modeling the chromosomal determinants of a quantitative trait will be useful only for traits with high heritabilities or when fine-scale genetic maps can be employed. Goldgar's technique as a whole has promise, as it can be made relatively robust statistically, refined through some simple and intuitive extensions, and can be easily adapted to work with more complex sampling units. Further extensions of Goldgar's methods are proposed, and areas in need of additional research are discussed.