Body composition (fat and lean compartments) and bone mineral density were measured in 246 healthy premenopausal women, aged 20-40 years, residing in Tecumseh, Michigan. Body composition was measured using four-point bioelectrical impedance and values for fat and lean compartments categorized into tertiles. Additionally, each woman was classified into one of nine different cells based on her location within a 3 x 3 table which reflects the joint distribution of both fat and lean compartments. Bone mineral density of the proximal femur, including the femoral neck and trochanter, was measured using dual photon densitometry. The mean femoral neck bone mineral density values increased significantly and linearly for each tertile of muscle mass (0.90, 0.95, and 1.02 g/cm2, p less than 0.0002). Femoral bone mineral density increased significantly but not linearly as the fat compartment progressed from the lowest to the highest tertile (0.95, 0.93, and 0.99 g/cm2). Bone mineral density of the proximal femur was similar and significantly greater in the high muscle/low fat and high muscle/high fat body composition subgroups compared with bone mineral density in the seven other groups. However, women in the high muscle/low fat subgroup had substantially lower mean weight (67 vs. 91 kg, p less than 0.0001) and mean Quetelet index (22.1 vs. 33.7 kg/m2, p less than 0.0001) than women in the high muscle/high fat subgroup. Bone mineral density values were similar and significantly lower in the following body composition cells: low muscle/low fat, low muscle/medium fat, and low muscle/high fat. Similar findings were observed at the trochanteric site. Low muscle is a risk factor for low bone mineral density in young adult women while higher fat is protective only when associated with substantial muscle.

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Summary This paper presents a method of discriminant analysis especially suited to longitudinal data. The approach is in the spirit of canonical variate analysis (CVA) and is similarly intended to reduce the dimensionality of multivariate data while retaining information about group differences. A drawback of CVA is that it does not take advantage of special structures that may be anticipated in certain types of data. For longitudinal data, it is often appropriate to specify a growth curve structure (as given, for example, in the model of Potthoff & Roy, 1964). The present paper focuses on this growth curve structure, utilizing it in a model‐based approach to discriminant analysis. For this purpose the paper presents an extension of the reduced‐rank regression model, referred to as the reduced‐rank growth curve (RRGC) model. It estimates discriminant functions via maximum likelihood and gives a procedure for determining dimensionality. This methodology is exploratory only, and is illustrated by a well‐known dataset from Grizzle & Allen (1969).

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