The main objective of this research is non-linear modeling of growth curve during kefir grains batch propagation. For this purpose some laboratory experiments were performed in an RC1 reactor provided data for growth curve construction. Afterwards, we fitted several growth models (Logistic, Gompertz and Richards) and compared their biological parameters. Finally, we established the statisticall...

A fundamental observation in the social and behavioral sciences is that people change over time, but not necessarily in the same way or at the same rate. For example, verbal ability increases steadily throughout the elementary school years, but it does not increase at the same rate for all students. There are individual differences in the rate and direction of change in many contexts, and these...

in the current study, two line with short-term divergent selection for high weight (hw) and low weight (lw) at 4 wk of age after 7 generation were analyzed in coturnix japonica quail. hw line was significantly higher than lw line at 28d of age (p<0.01). 21 females, and 11 male from the hw, 18 females plus 10 male from the lw lines were mated as reciprocal cross and within lines to produce hh, l...

Growth curve models are used to analyze repeated measures data (longitudinal data), which are functions of time. General expressions of weighted least-squares estimators (WLSEs) of parameter matrices were given under a general growth curve model. Some algebraic and statistical properties of the estimators are also derived through the matrix rank method. AMS subject classifications. 62F11, 62H12...

Learning and development are ubiquitous. When new skills are acquired, when attitudes and interests develop, people change. Measuring change demands a longitudinal perspective, with multiple waves of data collected on representative people at sensibly spaced intervals. Multi-wave data is usually analyzed by individual growth modeling using a multilevel model for change (Singer & Willett, 2003)....