A method is discussed which extends canonical regression analysis to the situation where the variables may be measured at a variety of levels (nominal, ordinal, or interval), and where they may be either continuous or discrete. There is no restriction on the mix of measurement characteristics (i.e., some variables may be discrete-ordinal, others continuous-nominal, and yet others discrete-interval). The method, which is purely descriptive, scales the observations on each variable, within the restriction imposed by the variable's measurement characteristics, so that the canonical correlation is maximal. The alternating least squares algorithm is discussed. Several examples are presented. It is concluded that the method is very robust. Inferential aspects of the method are not discussed.

Cross-classified data are frequently encountered in behavioral and social science research. The loglinear model and dual scaling (correspondence analysis) are two representative methods of analyzing such data. An alternative method, based on ideal point discriminant analysis (DA), is proposed for analysis of contingency tables, which in a certain sense encompasses the two existing methods. A variety of interesting structures can be imposed on rows and columns of the tables through manipulations of predictor variables and/or as direct constraints on model parameters. This, along with maximum likelihood estimation of the model parameters, allows interesting model comparisons. This is illustrated by the analysis of several data sets.

This study formulates a property of a quantification method, the principle of equivalent partitioning (PEP). When the PEP is used together with Guttman's principle of internal consistency (PIC) in a simple way, the combination offers an interesting way of analyzing categorical data in terms of the variate(s) chosen by the investigator, a type of canonical analysis. The study discusses applications of the technique to multiple-choice, rank-order, and paired comparison data.

A generalized least squares approach is presented for incorporating linear constraints on the standardized row and column scores obtained from a canonical analysis of a contingency table. The method is easy to implement and may simplify considerably the interpretation of a data matrix. The approach is compared to a restricted maximum likelihood procedure.

A formula for the determinant of a partitioned matrix, possibly with singular submatrices, is derived and applied to some psychometric and numerical problems.

The main purpose of the study was to compare the capacity of the major sheep breeds in Morocco to cope with climate changes through the ranges of several climate parameters in which they can be found. We first delimitated the climatic ‘domains’ of each breed by constructing a database including altitude and climatic parameters (minima mean of the coldest month, maxima mean of the hottest month, annual rainfall, pluviothermic coefficient of Emberger Q2, annual minima mean and annual maxima mean) on a 30-year period using the representative stations of each breed distribution. The overlap between each breed combination was quantified through a canonical analysis that extracted the most discriminant parameters. The variance analysis of each climatic parameter evidenced two breeds remarkable by their tolerance. The first one is the Timahdite, mainly settled in areas over 1100 m, which can tolerate the greatest variations in annual rainfall and pluviothermic coefficient. In spite of this feature, this breed is endangered owing to the decreasing quality of pastures. The second one is the D’man which apparently can support high variations in extreme temperatures. In fact, this breed is not well adapted to pastures and requires a special microclimate offered by oases. The information reported in this study will be the basis for the establishment of characterization and selection strategies for Moroccan sheep.

A total of 700 adult female goats from Sétif area (Algeria), were investigated for eight qualitative morphological traits and 17 body measurements. Sampling included three environmental areas: Northern, Central and Southern area. Coefficients of variation ranged from 10.9 percent to 34.7 percent, showing high heterogeneity. Canonical analyses showed that differences in body measurements between the three area-populations were large and significant in all traits (P < 0.001). The shortest Mahalanobis distance was found between North-Center populations (2.8), while that between Center (4.0) and (8.6) between North-South populations were the largest. Discriminant analysis showed that most goat-populations were classified into their environmental-area, North (73.0 percent), Center (66.8 percent) and South (79.3 percent) with a few misclassified individuals. Correspondence analysis indicated no large differences between the goat populations; they were more homogeneous for qualitative traits. This information will constitute the basis for further characterization and develop conservation strategies for Algerian goat populations

A visual image analysis (VIA) system provided continuous, automatic collection of size and shape data for a total of 116 pigs slaughtered serially from 25 to 115 kg live weight. Males and females of three types of pigs (‘Meishan’ type, ‘Pietrain’ type, and ‘Landrace’ type) were selected to provide variation in both composition and conformation (the three types being, respectively, ‘fat’, ‘blocky’, and ‘lean’). Results below are presented in this order. Regression analysis was used to relate VIA size to platform weigher (FIRE) measurements of live weight. Residual maximum likelihood (REML) analysis showed that at the observed growth rate, a change in pig state could be detected by VIA after 8, 9, and 10 days respectively for the three types, and by the platform weigher system after 12, 4, and 13 days (in both cases with a confidence of 95%). Artificial neural network and canonical variates analysis were used to test the ability of VIA to distinguish between pig types and sexes. With cross validation, the canonical variates analysis correctly classified the three types in 72, 83, and 64% of observations, and the neural network in 81, 81, and 64% of observations. The VIA system is considered to be a valuable monitoring system which may play a rôle in the construction of integrated management systems (IMS).

The shapes of cervical (C1–C7) and upper thoracic (T1, T2) vertebrae from the rat and the grey-headed flying fox have been analysed by Fourier analysis to investigate the types of variation present and to try to isolate bones according to position along the vertebral column and species. It was found that the T2 vertebrae of the rat are very different from all others in the study, that C2 and C6 vertebrae are very similar and that the remaining vertebrae split according to species.

The hierarchic behaviour of 71 goats of the Verata breed from two independent flocks on two different farms (no.2 = 34 and no. 2 = 37) was studied during the milking-period of a year. Two statistical procedures: canonical correspondence analysis (CCA) and a log-linear model were used. In the CCA, the total frequencies of each goat in each of the 12 positions at the milking stalls during 210 days of lactation were computed as original variables. Canonical variables were the average values of dairy milk production, proportion of protein and proportion of fat. The first two CCA axes accounted for proportionately 0·72 of the variance. The first axis showed the effect of rank order (V1 = 0·45) and the second axis the variability between animals for the same group of hierarchy (V2 = 0·27). The first position (AC1, = 0·58; AC2 = 0·23) and the last position (AC1 = 0·11; AC2 = 0·26) of the milking stalls were in absolute contributions the most significant in the distribution of the four observed groups of hierarchy, as defined by their frequency of access to the first position. Two parameters were highly correlated with both axes: milk protein content (r1, = - 0·8; r2 = 0·9) and the day milk production (r1 = 0·6; r2 = 0·5). These results showed a direct relationship between rank order and milk production, whereas the variability in each group was best defined by the protein content. The log-linear model showed that goats of lactation numbers one, two and three have a similar behaviour with respect to their locations at the milking stalls, being distributed more randomly (â1, = 0·68 < â2 = 0·7 < â3 = 0·71) than goats of a lactation number four (â4 = 2·95). This effect could be a consequence of two different but related factors: either the animals develop a preference for a particular position over time, or that animals in their fourth lactation showed a more stable behaviour pattern which affected their body condition.

Predicted rate of genetic response for multiple trait breeding objectives from multivariate analyses is compared with that from univariate analyses for a range of breeding schemes, A selection index that approximates a multipl trait best linear unbiased prediction (BLUP) animal model is utilized. Changes in genetic parameters due to linkage disequilibrium generated by selection are accounted for. This study shows that asymptotic response in the aggregate breeding value, and its component traits, to selection on multivariate predictions, can easily be calculated from first generation responses, which use ancestral information. For two-path breeding schemes with equal accuracy for males and females, proportional reductions in responses depend only on selection intensity. In general, benefit from multivariate over univariate analyses is slightly smaller at the asymptote than in the first generation. Multivariate analyses give substantially more response than univariate analyses on untransformed data, when correlations between traits are high and when genetic and phenotypic correlations have opposite signs. The advantage of multivariate analyses decreases with increasing family size. When three random factors (additive genetic, common and individual environmental effects) are included in the model, the benefit of multivariate analysis is negligible if univariate analyses are performed on canonical traits. In this case, the advantage of multivariate analyses is never higher than 1% for all cases studied. These results are of particular relevance to the design of genetic evaluation programmes.