## ABSTRACT

We covered a variety of approaches for modeling mean (and covariance) structure of data in the preceding chapters. For example, the classical linear regression model allowed us to infer how the heterogeneous mean of the data varies with predictor variables of interest. To do so, we parameterized a statistical model as
y
i
∼
N
(
x
i
′
β
,
σ
2
)
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, for i = 1, …, n, where
x
i
′
β
https://s3-euw1-ap-pe-df-pch-content-public-u.s3.eu-west-1.amazonaws.com/9780429243653/5e9d5048-c3be-4c1d-b567-ce1ed3c5444c/content/equ_551.tif"/>
represents the mean of the data distribution at covariate values x
_{i}
. However, while this regression model tells us something about the average relationship between x
_{i}
and y_{i}
, there could be other important aspects of the relationship that it does not provide inference about. For example, what if we are interested in learning about the relationship between x
_{i}
and y_{i}
associated with the median of the data, or even the upper or lower tail of the data?