This function checks the parameter inputs to the simulation functions nonnormsys,
corrsys, and corrsys2. It should be used prior to execution of these
functions to ensure all inputs are of the correct format. Those functions do not contain parameter checks in order to decrease
simulation time. This would be important if the user is running several simulation repetitions so that the inputs only have to
be checked once. Note that the inputs do not include all of the inputs to the simulation functions. See the appropriate function
documentation for more details about parameter inputs. Since the parameter input list is extensive and this function does not check
for all possible errors, if simulation gives an error, the user should still check the parameter inputs.
checkpar(M = NULL, method = c("Fleishman", "Polynomial"),
error_type = c("non_mix", "mix"), means = list(), vars = list(),
skews = list(), skurts = list(), fifths = list(), sixths = list(),
Six = list(), mix_pis = list(), mix_mus = list(), mix_sigmas = list(),
mix_skews = list(), mix_skurts = list(), mix_fifths = list(),
mix_sixths = list(), mix_Six = list(), marginal = list(),
support = list(), lam = list(), p_zip = list(), pois_eps = list(),
size = list(), prob = list(), mu = list(), p_zinb = list(),
nb_eps = list(), corr.x = list(), corr.yx = list(), corr.e = NULL,
same.var = NULL, subj.var = NULL, int.var = NULL, tint.var = NULL,
betas.0 = NULL, betas = list(), betas.subj = list(),
betas.int = list(), betas.t = NULL, betas.tint = list(),
rand.int = c("none", "non_mix", "mix"), rand.tsl = c("none", "non_mix",
"mix"), rand.var = NULL, corr.u = list(), quiet = FALSE)the number of dependent variables \(Y\) (outcomes); equivalently, the number of equations in the system
the PMT method used to generate all continuous variables, including independent variables (covariates), error terms, and random effects; "Fleishman" uses Fleishman's third-order polynomial transformation and "Polynomial" uses Headrick's fifth-order transformation
"non_mix" if all error terms have continuous non-mixture distributions, "mix" if all error terms have continuous mixture distributions
if no random effects, a list of length M where means[[p]] contains a vector of means for the continuous independent variables
in equation p with non-mixture (\(X_{cont}\)) or mixture (\(X_{mix}\)) distributions and for the error terms (\(E\));
order in vector is \(X_{cont}, X_{mix}, E\)
if there are random effects, a list of length M + 1 if the effects are the same across equations or 2 * M if they differ;
where means[M + 1] or means[(M + 1):(2 * M)] are vectors of means for all random effects with continuous non-mixture or mixture distributions;
order in vector is 1st random intercept \(U_0\) (if rand.int != "none"), 2nd random time slope \(U_1\) (if rand.tsl != "none"),
3rd other random slopes with non-mixture distributions \(U_{cont}\), 4th other random slopes with mixture distributions \(U_{mix}\)
a list of same length and order as means containing vectors of variances for the continuous variables, error terms, and any random effects
if no random effects, a list of length M where skews[[p]] contains a vector of skew values for the continuous independent variables
in equation p with non-mixture (\(X_{cont}\)) distributions and for \(E\) if error_type = "non_mix"; order in vector is \(X_{cont}, E\)
if there are random effects, a list of length M + 1 if the effects are the same across equations or 2 * M if they differ;
where skews[M + 1] or skews[(M + 1):(2 * M)] are vectors of skew values for all random effects with continuous non-mixture distributions;
order in vector is 1st random intercept \(U_0\) (if rand.int = "non_mix"), 2nd random time slope \(U_1\) (if rand.tsl = "non_mix"),
3rd other random slopes with non-mixture distributions \(U_{cont}\)
a list of same length and order as skews containing vectors of standardized kurtoses (kurtosis - 3) for the continuous variables,
error terms, and any random effects with non-mixture distributions
a list of same length and order as skews containing vectors of standardized fifth cumulants for the continuous variables,
error terms, and any random effects with non-mixture distributions; not necessary for method = "Fleishman"
a list of same length and order as skews containing vectors of standardized sixth cumulants for the continuous variables,
error terms, and any random effects with non-mixture distributions; not necessary for method = "Fleishman"
a list of length M, M + 1, or 2 * M, where Six[1:M] are for \(X_{cont}, E\) (if error_type = "non_mix") and
Six[M + 1] or Six[(M + 1):(2 * M)] are for non-mixture \(U\);
if error_type = "mix" and there are only random effects (i.e., length(corr.x) = 0), use Six[1:M] = rep(list(NULL), M) so that
Six[M + 1] or Six[(M + 1):(2 * M)] describes the non-mixture \(U\);
Six[[p]][[j]] is a vector of sixth cumulant correction values to aid in finding a valid PDF for \(X_{cont(pj)}\), the
j-th continuous non-mixture covariate for outcome \(Y_p\); the last vector in Six[[p]] is for \(E_p\) (if error_type = "non_mix");
use Six[[p]][[j]] = NULL if no correction desired for \(X_{cont(pj)}\);
use Six[[p]] = NULL if no correction desired for any continuous non-mixture covariate or error term in equation p
Six[[M + p]][[j]] is a vector of sixth cumulant correction values to aid in finding a valid PDF for \(U_{(pj)}\), the
j-th non-mixture random effect for outcome \(Y_p\); use Six[[M + p]][[j]] = NULL if no correction desired for \(U_{(pj)}\);
use Six[[M + p]] = NULL if no correction desired for any continuous non-mixture random effect in equation p
keep Six = list() if no corrections desired for all equations or if method = "Fleishman"
list of length M, M + 1 or 2 * M, where mix_pis[1:M] are for \(X_{cont}, E\) (if error_type = "mix") and
mix_pis[M + 1] or mix_pis[(M + 1):(2 * M)] are for mixture \(U\); use mix_pis[[p]] = NULL if equation p has no continuous mixture terms
if error_type = "non_mix" and there are only random effects (i.e., length(corr.x) = 0), use mix_pis[1:M] = NULL so that
mix_pis[M + 1] or mix_pis[(M + 1):(2 * M)] describes the mixture \(U\);
mix_pis[[p]][[j]] is a vector of mixing probabilities of the component distributions for \(X_{mix(pj)}\), the j-th mixture covariate for outcome \(Y_p\);
the last vector in mix_pis[[p]] is for \(E_p\) (if error_type = "mix"); components should be ordered as in corr.x
mix_pis[[M + p]][[j]] is a vector of mixing probabilities of the component distributions for \(U_{(pj)}\), the j-th random effect with a mixture distribution
for outcome \(Y_p\); order is 1st random intercept (if rand.int = "mix"), 2nd random time slope (if rand.tsl = "mix"),
3rd other random slopes with mixture distributions; components should be ordered as in corr.u
list of same length and order as mix_pis;
mix_mus[[p]][[j]] is a vector of means of the component distributions for \(X_{mix(pj)}\),
the last vector in mix_mus[[p]] is for \(E_p\) (if error_type = "mix")
mix_mus[[p]][[j]] is a vector of means of the component distributions for \(U_{mix(pj)}\)
list of same length and order as mix_pis;
mix_sigmas[[p]][[j]] is a vector of standard deviations of the component distributions for \(X_{mix(pj)}\),
the last vector in mix_sigmas[[p]] is for \(E_p\) (if error_type = "mix")
mix_sigmas[[p]][[j]] is a vector of standard deviations of the component distributions for \(U_{mix(pj)}\)
list of same length and order as mix_pis;
mix_skews[[p]][[j]] is a vector of skew values of the component distributions for \(X_{mix(pj)}\),
the last vector in mix_skews[[p]] is for \(E_p\) (if error_type = "mix")
mix_skews[[p]][[j]] is a vector of skew values of the component distributions for \(U_{mix(pj)}\)
list of same length and order as mix_pis;
mix_skurts[[p]][[j]] is a vector of standardized kurtoses of the component distributions for \(X_{mix(pj)}\),
the last vector in mix_skurts[[p]] is for \(E_p\) (if error_type = "mix")
mix_skurts[[p]][[j]] is a vector of standardized kurtoses of the component distributions for \(U_{mix(pj)}\)
list of same length and order as mix_pis; not necessary for method = "Fleishman";
mix_fifths[[p]][[j]] is a vector of standardized fifth cumulants of the component distributions for \(X_{mix(pj)}\),
the last vector in mix_fifths[[p]] is for \(E_p\) (if error_type = "mix")
mix_fifths[[p]][[j]] is a vector of standardized fifth cumulants of the component distributions for \(U_{mix(pj)}\)
list of same length and order as mix_pis; not necessary for method = "Fleishman";
mix_sixths[[p]][[j]] is a vector of standardized sixth cumulants of the component distributions for \(X_{mix(pj)}\),
the last vector in mix_sixths[[p]] is for \(E_p\) (if error_type = "mix")
mix_sixths[[p]][[j]] is a vector of standardized sixth cumulants of the component distributions for \(U_{mix(pj)}\)
a list of same length and order as mix_pis;
keep mix_Six = list() if no corrections desired for all equations or if method = "Fleishman"
p-th component of mix_Six[1:M] is a list of length equal to the total number of component distributions for the \(X_{mix(p)}\)
and \(E_p\) (if error_type = "mix");
mix_Six[[p]][[j]] is a vector of sixth cumulant corrections for the j-th component distribution (i.e., if there are 2
continuous mixture independent variables for \(Y_p\), where \(X_{mix(p1)}\) has 2 components and \(X_{mix(p2)}\) has 3
components, then length(mix_Six[[p]]) = 5 and mix_Six[[p]][[3]] would correspond to the 1st component of
\(X_{mix(p2)}\)); use mix_Six[[p]][[j]] = NULL if no correction desired for that component;
use mix_Six[[p]] = NULL if no correction desired for any component of \(X_{mix(p)}\) and \(E_p\)
q-th component of mix_Six[M + 1] or mix_Six[(M + 1):(2 * M)] is a list of length equal to the total number of component distributions for
the \(U_{mix(q)}\); mix_Six[[q]][[j]] is a vector of sixth cumulant corrections for the j-th component distribution; use
mix_Six[[q]][[j]] = NULL if no correction desired for that component;
use mix_Six[[q]] = NULL if no correction desired for any component of \(U_{mix(q)}\)
a list of length M, with the p-th component a list of cumulative probabilities for the ordinal variables
associated with outcome \(Y_p\) (use marginal[[p]] = NULL if outcome \(Y_p\) has no ordinal variables);
marginal[[p]][[j]] is a vector of the cumulative probabilities defining the marginal distribution of \(X_{ord(pj)}\),
the j-th ordinal variable for outcome \(Y_p\); if the variable can take r values, the vector will contain r - 1 probabilities
(the r-th is assumed to be 1); for binary variables, the probability is the probability of the 1st category, which has the smaller support value;
length(marginal[[p]]) can differ across outcomes; the order should be the same as in corr.x
a list of length M, with the p-th component a list of support values for the ordinal variables associated
with outcome \(Y_p\); use support[[p]] = NULL if outcome \(Y_p\) has no ordinal variables;
support[[p]][[j]] is a vector of the support values defining the marginal distribution of \(X_{ord(pj)}\),
the j-th ordinal variable for outcome \(Y_p\); if not provided, the default for r categories is 1, ..., r
list of length M, p-th component a vector of lambda (means > 0) values for Poisson variables for outcome \(Y_p\)
(see stats::dpois); order is 1st regular Poisson and 2nd zero-inflated Poisson; use lam[[p]] = NULL if outcome \(Y_p\) has no Poisson variables;
length(lam[[p]]) can differ across outcomes; the order should be the same as in corr.x
a list of vectors of probabilities of structural zeros (not including zeros from the Poisson distribution) for the
zero-inflated Poisson variables (see VGAM::dzipois); if p_zip = 0, \(Y_{pois}\) has a regular Poisson
distribution; if p_zip is in (0, 1), \(Y_{pois}\) has a zero-inflated Poisson distribution;
if p_zip is in (-(exp(lam) - 1)^(-1), 0), \(Y_{pois}\) has a zero-deflated Poisson distribution and p_zip
is not a probability; if p_zip = -(exp(lam) - 1)^(-1), \(Y_{pois}\) has a positive-Poisson distribution
(see VGAM::dpospois); order is 1st regular Poisson and 2nd zero-inflated Poisson;
if a single number, all Poisson variables given this value; if a vector of length M, all Poisson variables in equation p
given p_zip[p]; otherwise, missing values are set to 0 and ordered 1st
list of length M, p-th component a vector of length lam[[p]] containing cumulative probability truncation values
used to calculate intermediate correlations involving Poisson variables; order is 1st regular Poisson and 2nd zero-inflated Poisson;
if a single number, all Poisson variables given this value; if a vector of length M, all Poisson variables in equation p
given pois_eps[p]; otherwise, missing values are set to 0.0001 and ordered 1st
list of length M, p-th component a vector of size parameters for the Negative Binomial variables for outcome \(Y_p\)
(see stats::dnbinom); order is 1st regular NB and 2nd zero-inflated NB; use size[[p]] = NULL if outcome \(Y_p\) has no Negative Binomial variables;
length(size[[p]]) can differ across outcomes; the order should be the same as in corr.x
list of length M, p-th component a vector of success probabilities for the Negative Binomial variables for outcome \(Y_p\)
(see stats::dnbinom); order is 1st regular NB and 2nd zero-inflated NB; use prob[[p]] = NULL if outcome \(Y_p\) has no Negative Binomial variables;
length(prob[[p]]) can differ across outcomes; the order should be the same as in corr.x
list of length M, p-th component a vector of mean values for the Negative Binomial variables for outcome \(Y_p\)
(see stats::dnbinom); order is 1st regular NB and 2nd zero-inflated NB; use mu[[p]] = NULL if outcome \(Y_p\) has no Negative Binomial variables;
length(mu[[p]]) can differ across outcomes; the order should be the same as in corr.x; for zero-inflated NB variables,
this refers to the mean of the NB distribution (see VGAM::dzinegbin)
(*Note: either prob or mu should be supplied for all Negative Binomial variables, not a mixture)
a vector of probabilities of structural zeros (not including zeros from the NB distribution) for the zero-inflated NB variables
(see VGAM::dzinegbin); if p_zinb = 0, \(Y_{nb}\) has a regular NB distribution;
if p_zinb is in (-prob^size/(1 - prob^size), 0), \(Y_{nb}\) has a zero-deflated NB distribution and p_zinb
is not a probability; if p_zinb = -prob^size/(1 - prob^size), \(Y_{nb}\) has a positive-NB distribution (see
VGAM::dposnegbin); order is 1st regular NB and 2nd zero-inflated NB;
if a single number, all NB variables given this value; if a vector of length M, all NB variables in equation p
given p_zinb[p]; otherwise, missing values are set to 0 and ordered 1st
list of length M, p-th component a vector of length size[[p]] containing cumulative probability truncation values
used to calculate intermediate correlations involving Negative Binomial variables; order is 1st regular NB and 2nd zero-inflated NB;
if a single number, all NB variables given this value; if a vector of length M, all NB variables in equation p
given nb_eps[p]; otherwise, missing values are set to 0.0001 and ordered 1st
list of length M, each component a list of length M; corr.x[[p]][[q]] is matrix of correlations
for independent variables in equations p (\(X_{(pj)}\) for outcome \(Y_p\)) and q (\(X_{(qj)}\) for outcome \(Y_q\));
order: 1st ordinal (same order as in marginal), 2nd continuous non-mixture (same order as in skews),
3rd components of continuous mixture (same order as in mix_pis), 4th regular Poisson, 5th zero-inflated Poisson (same order as in lam),
6th regular NB, and 7th zero-inflated NB (same order as in size);
if p = q, corr.x[[p]][[q]] is a correlation matrix with nrow(corr.x[[p]][[q]]) = # \(X_{(pj)}\) for outcome \(Y_p\);
if p != q, corr.x[[p]][[q]] is a non-symmetric matrix of correlations where rows correspond to covariates for \(Y_p\)
so that nrow(corr.x[[p]][[q]]) = # \(X_{(pj)}\) for outcome \(Y_p\) and
columns correspond to covariates for \(Y_q\) so that ncol(corr.x[[p]][[q]]) = # \(X_{(qj)}\) for outcome \(Y_q\);
use corr.x[[p]][[q]] = NULL if equation q has no \(X_{(qj)}\); use corr.x[[p]] = NULL if equation p has no \(X_{(pj)}\)
input for nonnormsys only; a list of length M, where the p-th component is a 1 row matrix of correlations between \(Y_p\) and \(X_{(pj)}\);
if there are mixture variables and the betas are desired in terms of these (and not the components), then corr.yx
should be specified in terms of correlations between outcomes and non-mixture or mixture variables, and the number of columns of the matrices
of corr.yx should not match the dimensions of the matrices in corr.x; if the betas are desired in terms of
the components, then corr.yx should be specified in terms of correlations between outcomes and non-mixture or components of
mixture variables, and the number of columns of the matrices of corr.yx should match the dimensions of the matrices in corr.x;
use corr.yx[[p]] = NULL if equation p has no \(X_{(pj)}\)
correlation matrix for continuous non-mixture or components of mixture error terms
either a vector or a matrix; if a vector, same.var includes column numbers of corr.x[[1]][[1]]
corresponding to independent variables that should be identical across equations; these terms must have the same indices for all
p = 1, ..., M; i.e., if the 1st ordinal variable represents sex which should be the same for each equation, then
same.var[1] = 1 since ordinal variables are 1st in corr.x[[1]][[1]] and sex is the 1st ordinal variable, and
the 1st term for all other outcomes must also be sex;
if a matrix, columns 1 and 2 are outcome p and column index in corr.x[[p]][[p]] for 1st instance of variable,
columns 3 and 4 are outcome q and column index in corr.x[[q]][[q]] for subsequent instances of variable; i.e., if
1st term for all outcomes is sex and M = 3, then same.var = matrix(c(1, 1, 2, 1, 1, 1, 3, 1), 2, 4, byrow = TRUE); the
independent variable index corresponds to ordinal, continuous non-mixture, component of continuous mixture, Poisson, or
NB variable
matrix where 1st column is outcome index (p = 1, ..., M), 2nd column is independent variable index
corresponding to covariate which is a a subject-level term (not including time), including time-varying covariates;
the independent variable index corresponds to ordinal, continuous non-mixture, continuous mixture (not mixture component), Poisson, or
NB variable; assumes all other variables are group-level terms; these subject-level terms are used to form interactions with the group
level terms
matrix where 1st column is outcome index (p = 1, ..., M), 2nd and 3rd columns are indices
corresponding to independent variables to form interactions between; this includes all interactions that are not accounted for by
a subject-group level interaction (as indicated by subj.var) or by a time-covariate interaction (as indicated by
tint.var); ex: 1, 2, 3 indicates that for outcome 1, the 2nd and 3rd independent variables form an interaction term;
the independent variable index corresponds to ordinal, continuous non-mixture, continuous mixture (not mixture component), Poisson, or
NB variable
matrix where 1st column is outcome index (p = 1, ..., M), 2nd column is index of
independent variable to form interaction with time; if tint.var = NULL or no \(X_{(pj)}\) are indicated for outcome \(Y_p\),
this includes all group-level variables (variables not indicated as subject-level variables in subj.var), else includes only
terms indicated by 2nd column (i.e., in order to include subject-level variables);
ex: 1, 1 indicates that for outcome 1, the 1st independent variable has an interaction with time;
the independent variable index corresponds to ordinal, continuous non-mixture, continuous mixture (not mixture component), Poisson, or
NB variable
vector of length M containing intercepts, if NULL all set equal to 0; if length 1, all intercepts set to
betas.0
list of length M, p-th component a vector of coefficients for outcome \(Y_p\), including group and subject-level terms;
order is order of variables in corr.x[[p]][[p]]; if betas = list(), all set to 0 so that all \(Y\) only have intercept
and/or interaction terms plus error terms; if all outcomes have the same betas, use list of length 1; if \(Y_p\) only has intercept
and/or interaction terms, set betas[[p]] = NULL; if there are continuous mixture variables, beta is for mixture variable
(not for components)
list of length M, p-th component a vector of coefficients for interaction terms between group-level terms and
subject-level terms given in subj.var; order is the same order as given in subj.var; if all outcomes have the same betas,
use list of length 1; if \(Y_p\) only has group-level terms, set betas.subj[[p]] = NULL;
if there are continuous mixture variables, beta is for mixture variable (not for components)
list of length M, p-th component a vector of coefficients for interaction terms indicated in int.var;
order is the same order as given in int.var; if all outcomes have the same betas, use list of length 1;
if \(Y_p\) has none, set betas.int[[p]] = NULL;
if there are continuous mixture variables, beta is for mixture variable (not for components)
vector of length M of coefficients for time terms, if NULL all set equal to 1;
if length 1, all intercepts set to betas.t
list of length M, p-th component a vector of coefficients for interaction terms indicated in tint.var;
order is the same order as given in tint.var; if all outcomes have the same betas, use list of length 1;
if \(Y_p\) has none, set betas.tint[[p]] = NULL;
if there are continuous mixture variables, beta is for mixture variable (not for components)
"none" (default) if no random intercept term for all outcomes, "non_mix" if all random intercepts have a continuous
non-mixture distribution, "mix" if all random intercepts have a continuous mixture distribution;
also can be a vector of length M containing a combination (i.e., c("non_mix", "mix", "none") if the 1st has a non-mixture
distribution, the 2nd has a mixture distribution, and 3rd outcome has no random intercept)
"none" (default) if no random slope for time for all outcomes, "non_mix" if all random time slopes have a
continuous non-mixture distribution, "mix" if all random time slopes have a continuous mixture distribution; also can
be a vector of length M as in rand.int
matrix where 1st column is outcome index (p = 1, ..., M), 2nd column is independent variable index
corresponding to covariate to assign random effect to (not including the random intercept or time slope if present);
the independent variable index corresponds to ordinal, continuous non-mixture, continuous mixture (not mixture component), Poisson, or
NB variable; order is 1st continuous non-mixture and 2nd continuous mixture random effects; note that the order of the rows corresponds
to the order of the random effects in corr.u not the order of the
independent variable so that a continuous mixture covariate with a non-mixture random effect would be ordered before a
continuous non-mixture covariate with a mixture random effect (the 2nd column of rand.var indicates the specific covariate)
if the random effects are the same variables across equations, a matrix of correlations for \(U\);
if the random effects are different variables across equations, a list of length M, each component a list of length M;
corr.u[[p]][[q]] is matrix of correlations for random effects in equations p (\(U_{(pj)}\) for outcome \(Y_p\)) and
q (\(U_{(qj)}\) for outcome \(Y_q\));
if p = q, corr.u[[p]][[q]] is a correlation matrix with nrow(corr.u[[p]][[q]]) = # \(U_{(pj)}\) for outcome \(Y_p\);
if p != q, corr.u[[p]][[q]] is a non-symmetric matrix of correlations where rows correspond to \(U_{(pj)}\) for \(Y_p\)
so that nrow(corr.u[[p]][[q]]) = # \(U_{(pj)}\) for outcome \(Y_p\) and
columns correspond to \(U_{(qj)}\) for \(Y_q\) so that ncol(corr.u[[p]][[q]]) = # \(U_{(qj)}\) for outcome \(Y_q\);
the number of random effects for \(Y_p\) is taken from nrow(corr.u[[p]][[1]]) so that if there should be random effects,
there must be entries for corr.u;
use corr.u[[p]][[q]] = NULL if equation q has no \(U_{(qj)}\); use corr.u[[p]] = NULL if equation p has no \(U_{(pj)}\);
correlations are specified in terms of components of mixture variables (if present);
order is 1st random intercept (if rand.int != "none"), 2nd random time slope (if rand.tsl != "none"),
3rd other random slopes with non-mixture distributions, 4th other random slopes with mixture distributions
if FALSE prints messages, if TRUE suppresses messages
TRUE if all inputs are correct, else it will stop with a correction message
Headrick TC, Beasley TM (2004). A Method for Simulating Correlated Non-Normal Systems of Linear Statistical Equations. Communications in Statistics - Simulation and Computation, 33(1). 10.1081/SAC-120028431
# NOT RUN {
# Example: system of three equations for 2 independent variables, where each
# error term has unit variance, from Headrick & Beasley (2002)
# Y_1 = beta_10 + beta_11 * X_11 + beta_12 * X_12 + sigma_1 * e_1
# Y_2 = beta_20 + beta_21 * X_21 + beta_22 * X_22 + sigma_2 * e_2
# Y_3 = beta_30 + beta_31 * X_31 + beta_32 * X_32 + sigma_3 * e_3
# X_11 = X_21 = X_31 = Exponential(2)
# X_12 = X_22 = X_32 = Laplace(0, 1)
# e_1 = e_2 = e_3 = Cauchy(0, 1)
M <- 3
Stcum1 <- calc_theory("Exponential", 2)
Stcum2 <- calc_theory("Laplace", c(0, 1))
Stcum3 <- c(0, 1, 0, 25, 0, 1500) # taken from paper
means <- lapply(seq_len(M), function(x) c(0, 0, 0))
vars <- lapply(seq_len(M), function(x) c(1, 1, 1))
skews <- lapply(seq_len(M), function(x) c(Stcum1[3], Stcum2[3], Stcum3[3]))
skurts <- lapply(seq_len(M), function(x) c(Stcum1[4], Stcum2[4], Stcum3[4]))
fifths <- lapply(seq_len(M), function(x) c(Stcum1[5], Stcum2[5], Stcum3[5]))
sixths <- lapply(seq_len(M), function(x) c(Stcum1[6], Stcum2[6], Stcum3[6]))
corr.yx <- list(matrix(c(0.4, 0.4), 1), matrix(c(0.5, 0.5), 1),
matrix(c(0.6, 0.6), 1))
corr.x <- list()
corr.x[[1]] <- corr.x[[2]] <- corr.x[[3]] <- list()
corr.x[[1]][[1]] <- matrix(c(1, 0.1, 0.1, 1), 2, 2)
corr.x[[1]][[2]] <- matrix(c(0.1974318, 0.1859656, 0.1879483, 0.1858601),
2, 2, byrow = TRUE)
corr.x[[1]][[3]] <- matrix(c(0.2873190, 0.2589830, 0.2682057, 0.2589542),
2, 2, byrow = TRUE)
corr.x[[2]][[1]] <- t(corr.x[[1]][[2]])
corr.x[[2]][[2]] <- matrix(c(1, 0.35, 0.35, 1), 2, 2)
corr.x[[2]][[3]] <- matrix(c(0.5723303, 0.4883054, 0.5004441, 0.4841808),
2, 2, byrow = TRUE)
corr.x[[3]][[1]] <- t(corr.x[[1]][[3]])
corr.x[[3]][[2]] <- t(corr.x[[2]][[3]])
corr.x[[3]][[3]] <- matrix(c(1, 0.7, 0.7, 1), 2, 2)
corr.e <- matrix(0.4, nrow = 3, ncol = 3)
diag(corr.e) <- 1
checkpar(M, "Polynomial", "non_mix", means, vars, skews,
skurts, fifths, sixths, corr.x = corr.x, corr.yx = corr.yx,
corr.e = corr.e, quiet = TRUE)
# }
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