# semLme: Linear Mixed Regression with Interval Censored Dependent... In smicd: Statistical Methods for Interval Censored Data

## Description

This function estimates the linear mixed regression model when the dependent variable is interval censored. The estimation of the standard errors is fasciliated by a parametric bootstrap.

## Usage

 ```1 2``` ```semLme(formula, data, classes, burnin = 40, samples = 200, trafo = "None", adjust = 2, bootstrap.se = FALSE, b = 100) ```

## Arguments

 `formula` a two-sided linear formula object describing both the fixed-effects and random-effects part of the model, with the response on the left of a ~ operator and the terms, separated by + operators, on the right. Random-effects terms are distinguished by vertical bars (|) separating expressions for design matrices from grouping factors, as in `lmer`. Note: Only random intercept and random slope models are implemented at that point (e.g. ```y ~ x + (1| ID)```, or `y ~ x + (x|ID)`). The dependent variable is measuread as interval censored values; factor with ordered factor values `data` a data frame containing the variables of the model `classes` numeric vector of classes; `-Inf` as lower interval bound and `Inf` as upper interval bound is allowed. If the Box-Cox or logarithmic transformation is chosen, the minimum interval bound must be ≥ 0. `burnin` the number of burn-in iterations of the SEM-algorithm `samples` the number of additional iterations of the SEM-algorithm for parameter estimation `trafo` transformation of the dependent variable to fulfil the model assumptions "log" for Logarithmic transformation "bc" for Box-Cox transformation default is `"None"`. Transformations can only be used if the minimum interval bound is ≥ 0. `adjust` extends the number of iteration steps of the SEM-algorithm for finding the optimal lambda of the Box-Cox transformation. The number of iterations is extended in the following way: `(burnin+samples)*adjust` `bootstrap.se` if `TRUE` standard errors of the regression parameters are estimated `b` number of bootstrap iterations for the estimation of the standard errors

## Details

The model parameters are estimated using pseudo samples of the interval censored dependent variable. The object `pseudo.y` returns the pseudo samples of each iteration step of the SEM-algorithm.

## Value

An object of class "sem" that provides parameter estimated for linear regression models with interval censored dependent variable. Generic functions such as, `print`, `plot`, and `summary` have methods that can be used to obtain further information. See `semObject` for descriptions of components of objects of class "sem".

## References

Walter, P., Gross, M., Schmid, T. and Tzavidis, N. (2017). Estimation of Linear and Non-Linear Indicators using Interval Censored Income Data. FU-Berlin School of Business & Economics, Discussion Paper.

`lmer`, `print.sem`, `plot.sem`, `summary.sem`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17``` ```## Not run: # Load and prepare data data <- Exam classes <- c(1,1.5,2.5,3.5,4.5,5.5,6.5,7.7,8.5, Inf) data\$examsc.class<- cut(data\$examsc, classes) # Run model with random intercept and default settings model1 <- semLme(formula = examsc.class ~ standLRT + schavg + (1|school), data = data, classes = classes) summary(model1) # Run model with random intercept + random slope with default settings model2 <- semLme(formula = examsc.class ~ standLRT + schavg + (standLRT|school), data = data, classes = classes) summary(model2) ## End(Not run) ```