Motivated by the limited available literature on the treatment of longitudinal binary and ordinal outcomes in a growth modeling framework, the goal of this entry is to provide an accessible and practical introduction of this topic for a criminological audience. The parameterization of categorical latent growth models is explained by integrating aspects of the more familiar conventional latent g...

the Environmental Kuznets Curve (EKC) hypothesis postulates an inverted U-shaped relationship between economic growth and many local environmental health indicators, while some economists argue that the relationship follows other patterns. By using an overlapping generations (OLG) model, we focus on technological effects, where the properties of the existing pollution abatement technologies cou...

Four residuals in the MLNM(A1B1C1 + A2B2C2) are defined. The estimated model which is obtained by using the maximum likelihood theory is considered. The vec operator is applied to the estimated model and it turns out that the estimated model is the projection of the observations on the space generated by the design matrices which is the sum of two tensor product spaces. The estimated model is s...

The growth curve model (GCM), also known as GMANOVA, is a useful technique for investigating patterns of change in repeated measurement data over time and examining the effects of predictor variables on temporal trajectories. The reduced rank feature had been introduced previously to GCM for capturing redundant information in the criterion variables in a parsimonious way. In this paper, a ridge...

Objectives. To develop fundal height (FH) growth curve from normal singleton pregnancy based on last menstrual period (LMP) and/or ultrasound dating for women in the northern part of Thailand. Methods. A retrospective time-series study was conducted at four hospitals in the upper northern part of Thailand between January 2009 and March 2011. FH from 20 to 40 weeks was measured in centimeters. T...

The yield curve, which plots the yield of Treasury bonds against their maturity, is one of the most closely watched financial indicators.1 Many market observers carefully track the yield curve’s shape, which is typically upward sloping and somewhat convex. At times, however, it becomes flat or slopes downward (“inverts,” in Wall Street parlance), configurations that many business economists, fi...

Several sigmoidal functions (logistic, Gompertz, Richards, Schnute, and Stannard) were compared to describe a bacterial growth curve. They were compared statistically by using the model of Schnute, which is a comprehensive model, encompassing all other models. The t test and the F test were used. With the t test, confidence intervals for parameters can be calculated and can be used to distingui...

A fundamental aspect of predictive microbiology is the shape of the microbial growth curve and many models are used to fit microbial count data, the modified Gompertz and Baranyi equation being two of the most widely used. Rapid, automated methods such as turbidimetry have been widely used to obtain growth parameters, but do not directly give the microbial growth curve. Optical density (OD) dat...

Despite the widespread popularity of growth curve analysis, few studies have investigated robust growth curve models. In this paper, the t distribution is applied to model heavy-tailed data and contaminated normal data with outliers for growth curve analysis. The derived robust growth curve models are estimated through Bayesian methods utilizing data augmentation and Gibbs sampling algorithms. ...