satunnaistekijämalli

Satunnaistekijämalli, known in English as the random effects model, is a statistical model used in the analysis of hierarchical or clustered data. It accounts for the fact that observations within the same group are likely to be more similar to each other than observations from different groups. This similarity is captured by introducing a random variable for each group, which represents the deviation of that group's average effect from the overall population average.

The core idea is to partition the total variation in the data into variation between groups and variation within groups. In contrast to fixed effects models, where group-specific effects are treated as unknown constants to be estimated, random effects models assume these effects are drawn from a distribution, typically a normal distribution with a mean of zero and a certain variance. This assumption allows for generalization beyond the specific groups observed in the sample.

Random effects models are particularly useful when the groups are considered a random sample from a larger population, and the interest is in the variability between these groups. Applications are found across various fields, including econometrics, psychology, education, and public health, where data often exhibits a natural grouping structure, such as students within schools, patients within hospitals, or repeated measurements on individuals. The model provides estimates for both the overall average effect and the variance of the group-specific effects, offering insights into the extent of heterogeneity across groups.