Overview of the Mixed Model Personality
The Mixed Model personality of the Fit Model platform enables you to analyze models with complex covariance structures. The situations that can be analyzed include:
• Split plot experiments
• Random coefficients models
• Repeated measures designs
• Spatial data
• Correlated response data
Split plot experiments are experiments with two or more levels, or sizes, of experimental units resulting in multiple error terms. Such designs are often necessary when some factors are easy to vary and others are more difficult to vary. See Custom Designs in the Design of Experiments Guide.
Random coefficients models are also known as hierarchical or multilevel models (Singer 1998; Sullivan et al. 1999). These models are used when batches or subjects are thought to differ randomly in intercept and slope. Drug stability trials in the pharmaceutical industry and individual growth studies in educational research often require random coefficient models.
Repeated measures designs, spatial data, and correlated response data share the property that observations are not independent, requiring that you model their correlation structure.
• Repeated measures designs, also known as within-subject designs, model changes in a response over time or space while allowing errors to be correlated.
• Spatial data are measurements made in two or more dimensions, typically latitude and longitude. Spatial measurements are often correlated as a function of their spatial proximity.
• Correlated response data result from making several measurements on the same experimental unit. For example, height, weight, and blood pressure readings taken on individuals in a medical study, or hardness, strength, and elasticity measured on a manufactured item, are likely to be correlated. Although these measurements can be studied individually, treating them as correlated responses can lead to useful insights.
Failure to account for correlation between observations can result in incorrect conclusions about treatment effects. However, estimating covariance structure parameters uses information in the data. The number of parameters being estimated impacts power and the Type I error rate. For this reason, you must choose covariance models judiciously. See Example of Repeated Measures.