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Mixed Effects Models

A mixed model is a statistical model containing both fixed effects and random effects. These models are useful in the physical, biological and social sciences. They are particularly useful in settings where repeated measurements are made on the same statistical units or where measurements are made on clusters of related statistical units. Due to their advantage to deal with missing values, mixed effect models are often preferred over the traditional approaches such as repeated measures ANOVA.

The matrix notation a mixed model can be represented as is:

y = Xβ + Zμ + Ɛ


y is a vector of observations

β is a vector of fixed effects

μ is a vector of random effects

Ɛ is a vector of IID random error terms

X and Z are matrices of regressors relating the observations y to β and μ

Hypothesis Testing, Regression Analysis and ANOVA

Use the following information from a normal population with mean μ = 52 and variance σ2 = 22.5 to calculate the following questions. find P (X >55 ) find P (50≤X≤60) find P (X≤55) A random sample from a population with mean and standard deviation produced the following sample information: n =110 x = 6

Williams Corporation: Defective pricing

Williams Corporation Your contracting activity negotiated a $7,500,000 sole-source contract with the Williams Corporation about eight months ago. After the close of negotiations, Williams signed a Certificate of Current Cost or Pricing Data. During an audit for a follow-on contract, a Government technical expert identified an