This Ph.D. thesis primarily addresses the problem of testing the goodness of
fit for linear mixed models. The thesis introduces a novel method that is both
theoretically sound and supported by several simulations and a practical
example. The proposed method is based on two families of stochastic processes,
each with one primary and several secondary processes used to test the null
hypothesis. Additionally, the thesis demonstrates how similar methods with one
primary and multiple secondary stochastic processes can be adapted for
different statistical models by examining the goodness of fit of a linear
regression model using two slightly simpler methods. Overall, this thesis
presents a valuable contribution to statistical modeling by introducing a new
method for testing the goodness of fit of linear mixed models and exploring
its potential applications to other linear models.
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