build_dataset: Generate a multilevel long-form data frame
In L-Ippel/SEMA: Streaming Expectation Maximization Approximation

Description Usage Arguments Details Value Examples

This function builds a long-form data set with n observations from j units.

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build_dataset(n, j, fixed_coef, random_coef_sd, resid_sd,
  n_level_2_var = 2, mean_fixed_level_2 = 0, sd_fixed_level_2 = 1,
  mean_fixed_level_1 = 0, sd_fixed_level_1 = 1)

`n`	Number of observations.
`j`	Number of individuals.
`fixed_coef`	Vector with fixed effects coefficients.
`random_coef_sd`	Vector with standard deviations of the random effects.
`resid_sd`	Scalar, residual variance.
`n_level_2_var`	Number of level 2 variables.
`mean_fixed_level_2`	Means of the fixed effects covariates, level 2.
`sd_fixed_level_2`	Standard Deviation of the fixed effects covariates, level 2.
`mean_fixed_level_1`	Means of the fixed effects covariates, level 1.
`sd_fixed_level_1`	Standard deviation of the fixed effects covariates, level 1.

The function creates a data frame containing variables id, y, and V# with the number of fixed effects. The user can specify the number of level 2 covariates. The data are generated in two steps, first the level 2 data are generated, which are constant per unit then the ordering of units is created using the sample function, with replace = TRUE. This results in unequal number of observations per unit, altough each unit has equal probabilty of being sampled. Lastly, level 1 data are generated by drawing from the normal distribution.

A data frame with variable id, which labels the units, y is the outcome or dependent variable and covariates.

## We create a dataset, consisting of 2500 observations from 20 
## units. The fixed effects have the coefficients 1, 2, 3, 4, and 5. The 
## variance of the random effects equals 1, 4, and 9. Lastly the 
## residual variance equals 4:
  
test_data <- build_dataset(n = 2500, 
                           j = 20, 
                           fixed_coef = 1:5, 
                           random_coef_sd = 1:3, 
                           resid_sd = 2)