Given the knowledge of data, a researcher will be able to develop a statistical model that describes the environmental factors likely to influence the trait of interest. For example, the environmental factors that might affect milk yield per lactation include level of herd management, level of feeding, health status of animal, age of cow at calving, season in which the cow calved etc. Some of the environmental factors will be used in the model as discrete variables, others as continuous variables. Some fixed effects influence data but are in themselves of little interest. Data are corrected for them and no explicit estimates are obtained for such factors. However, there are some effects (e.g. trends in the year or differences in sexes) whose estimates may be of interest. For these, both the fixed and random effects are estimated and predicted simultaneously using the mixed model procedures.

Parameter estimates for the fixed effects of the model are obtained most often using least squares techniques (Searle, 1971). Once the parameters have been estimated, tests can be carried out to determine whether or not the factors included in the model account for significant variation in the quantitative trait measured. The best models for evaluating fixed effects are those that take into account all the other effects in the model when estimating parameters for a given effect. In addition, estimation of linear functions and testing hypotheses related to those functions are carried out. Given the effect of season of calving, for example, one may want to test that milk yield for cows calving in the wet or cold season such as winter differs from those calving in the dry season or in the summer. The average yields for the two seasons and also differences between these yield levels can be estimated. The next step is to test the hypothesis whether seasonal differences are important for such a trait [see Biometrics example 2]. In this example, least squares analysis fitting fixed effects (discrete and continuous) is illustrated. The steps followed are: calculation of descriptive statistics, development of the model and estimation of parameters for the fixed effects.

Once the importance of environmental factors has been established, records can be corrected or adjusted for these factors before proceeding to estimate genetic effects and parameters. Procedures, such as Best Linear Unbiased Prediction (BLUP) estimate parameters for environmental factors, adjust the data for these factors and estimate genetic effects simultaneously. BLUP stands for **Best- **because it maximizes the correlation between true and predicted breeding values (or minimizes the prediction error variance); **Linear** – predictions are linear functions of observations; **Unbiased** – estimation of realized values for a random variable such as animal breeding values and of estimable functions of fixed effects are unbiased; **Prediction** – involves prediction of true breeding value [BLUP]. A variety of computer software are available at minimal or no cost to facilitate data evaluation using BLUP procedures [Computer Software].