Generate simulated data

Generate simulated data from high dimensional genelized nonlinear factor model.

gendata(seed = 1, n = 300, p = 50,
              type =  c('homonorm', 'heternorm',
              'pois', 'bino', 'norm_pois', 'pois_bino', 'npb'),
                     q = 6, rho = 1, n_bin=1)

Arguments

seed: a nonnegative integer, the random seed, default as 1.
n: a positive integer, the sample size.
p: an positive integer, the variable dimension.
type: a character, specify the variables types for generated data, default as 'homonorm', representing the homogeneous gaussian variables.
q: a positive integer, the number of factors.
rho: a positive number, controlling the magnitude of loading matrix.
n_bin: a positive integer, specify the number of trails for the binomial variables when type is set to one of 'bino', 'pois_bino' and 'npb'.

Details

This function provides a variaty of mix of different variable types, in which 'homonorm' represents the generated data with only homogenous normal variables; 'heternorm' represents the data with only heterogenous normal variables; 'pois' means the data with only poisson variables; 'bino' means the data with only binomial variables; 'norm_pois' means the mix of normal and poisson variables; 'pois_bino' represents the mix of poisson and binomial variables; and 'npb' means the most complex mix of normal, poisson and binomial variables.

Value

return a list including two components:

X: a n-by-p matrix, the observed data matrix.
XList: a list consisting of the above observed data matrices with the same rows n (observations), and different columns (p1,p2, ..., p_d) and p columns in total, where d is the types of variables, pj is the dimension of varibles with the j-th type.
H0: a n-by-q matrix, the true lantent factor matrix.
B0: a p-by-q matrix, the true loading matrix, the last pzero rows are vectors of zeros.
mu0: a p-dimensional vector, the true intercept terms.

Author

Wei Liu

Note

nothing

Examples