Graphical approaches to support the analysis of linear-multilevel models of lamb pre-weaning growth in Kolda (Senegal) - Lancelot, R.; Lesnoff, Matthieu; Tillard, E.; McDermott, John J. (Elsevier, 2000)
Linear-multilevel models (LMM) are mixed-effects models in which several levels of grouping may be specified (village, herd, animal, ...). This study highlighted the usefulness of graphical methods in their analysis through: (1) the choice of the fixed and random effects and their structure, (2) the assessment of goodness-of-fit and (3) distributional assumptions for random effects and residuals. An AMM was developed to study the effect of ewe deworming with morantel on lamb preweaning growth in a field experiment involving 182 lambs in 45 herds 10 villages in Kolda, Senegal. Growth was described as a quadratic polynomial of age. Other covariates were sex, litter-size and treatment. The choice of fixed and random effects relied on three graphs: (1) a trellis display of mean live-weight vs. age, to select main effects and interactions (fixed effects): (2) a trellis display of individual growth curves, to decide which growth-curve terms should be included as random effects and (3) a scatter plot of parmaeters of lamb-specific regressions (live-weight vs. quadratic polynomial of age) to choose the random-effects covariance structure. Age, litter-size, age x litter-size, litter-size x treatment and age x litter-size x treatment were selected graphically as fixed effects and were significant (p<0.05) in subsequent statistical models. The selection of random-effect structures was guided by graphical assessment and comparison of the Akaike's information criterion for different models. The final random-effects selected included no random effect at the village level but intercept, age and squared-age at the herd and lamb levels. The structure of the random-effects variance-covariance matrices were blocked-diagonal at the herd level and unstructured at the lamb level. An order-1 autoregressive structure was retained to account for serial correlations of residuals. Smaller residual variance at 90 days tha at younger ages was modeled with a dummy variable taking a value of 1 at 90 days and 0 elsewhere. Ewe-deworming with morantel during the rainy season lead to higher lamb live-weights (probably related to a better ewe-nutrition and -health status). A positive correlation was demonstrated between early weight and growth rate at the population level (with important lamb and herd-level random deviations). The persistence of this correlation at older ages should be checked to determine whether early weights are good predictors of mature weights and ewe-reproductive lifetime performance.