טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentWeiss Sivan
SubjectStatistical Methods for Analyzing Multilevel Data
DepartmentDepartment of Industrial Engineering and Management
Supervisor Ms. Ayala Cohen (Deceased)


Abstract

One way to analyze hierarchical data is by using  the  mixed model.

The mixed model enables one to perform statistical inference on variables that were measured for different levels of the hierarchy, and it can take into account the dependency between measurements that belong to the same group.

Repeated measurements data are a special case of hierarchical data: measurements at different times are the lowest level and the subject and its characteristics represent the higher level.

This current study includes data analysis of children's height. The height measurements were taken several times during the age interval 0-4 years.

 In recent research it was  found that a bi-exponential model could describe growth data between the ages 0-4 years.

In the current  study a bi-exponential model with mixed effects was fitted to the growth data and applications of this model were demonstrated.

Two methods were used to fit the model. In the first, a fixed effects model was fitted to each subject separately and then the individual estimates were pooled to derive the estimates of the population. For the second method the NLMIXED procedure of SAS was used.

Applications  of the model include presentations of the velocity acceleration curves, estimation of percentiles of heights at age t and confidence intervals based on estimates of the variance of the growth curve.

The variance of the characteristic growth curve was estimated using the Delta method and the bootstrap.

The main conclusions of the research are:

1.                  A bi-exponential model with random effects can properly describe growth data for ages of 0-4 years.

2.                  The NLMIXED procedure was found to be better than the “individual estimates” method for fitting a nonlinear mixed model to the current data.

We suggest further research that will examine the robustness to the normality assumption of the random effects.