The main function of the package is to perform backward selection of fixed effects, forward fitting of the random effects, and post-hoc analysis using parallel capabilities. Other functionality includes the computation of ANOVAs with upper- or lower-bound p-values and R-squared values for each model term, model criticism plots, data trimming on model residuals, and data visualization. The data to run examples is contained in package LCF_data.

Bootstrap routines for nested linear mixed effects models fit using
    either 'lme4' or 'nlme'. The provided 'bootstrap()' function implements the
    parametric, residual, cases, random effect block (REB), and wild bootstrap 
    procedures. An overview of these procedures can be found 
    in Van der Leeden et al. (2008) <doi: 10.1007/978-0-387-73186-5_11>, 
    Carpenter, Goldstein & Rasbash (2003) <doi: 10.1111/1467-9876.00415>,
    and Chambers & Chandra (2013) <doi: 10.1080/10618600.2012.681216>.

We provide a solution for performing permutation tests on linear and mixed linear regression models. It
             allows users to obtain accurate p-values without making distributional assumptions about the data. By 
             generating a null distribution of the test statistics through repeated permutations of the response variable,
             permutation tests provide a powerful alternative to traditional parameter tests (Holt et al. (2023) 
             <doi:10.1007/s10683-023-09799-6>). In this early version, we focus on the permutation tests over observed 
             t values of beta coefficients, i.e.original t values generated by parameter tests. After generating a null 
             distribution of the test statistic through repeated permutations of the response variable, each observed t 
             values would be compared to the null distribution to generate a p-value. To improve the efficiency,a stop 
             criterion (Anscombe (1953) <doi:10.1111/j.2517-6161.1953.tb00121.x>) is adopted to force permutation to stop 
             if the estimated standard deviation of the value falls below a fraction of the estimated p-value. By doing so,
             we avoid the need for massive calculations in exact permutation methods while still generating stable and accurate 
             p-values.