FleishmanIC

skew

kurt

<p>The function are adapted from online support of the SAS system,
  URL: support.sas.com/publishing/authors/extras/65378_Appendix_D_Functions_for_Simulating_Data_by_Using_Fleishmans_Transformation.pdf
<code>FleishmanIC</code> produce an initial guess of the Fleishman coefficients from given skewness and kurtosis. It is to use for Newton's algorithm. 
 This guess is produced by a polynomial regression.</p>

The composites are linear combinations of their indicators in composite based structural equation models. Structural models are considered consisting of two blocks. The indicators of the exogenous composites are named by X, the indicators of the endogenous by Y. Reflective relations are given by arrows pointing  from the composite to their indicators. Their values are called loadings.  In a reflective-reflective scenario all indicators have loadings. Arrows are pointing to their indicators only from the endogenous composites in  the formative-reflective scenario. There are no loadings at all in the formative-formative scenario. The covariance matrices are computed for these three scenarios. They can be used to simulate these models. These models can also be estimated and a segmentation procedure is included as well.

Rainer Schlittgen

cbsem

Simulation, Estimation and Segmentation of Composite Based
Structural Equation Models

FleishmanIC function

Functions to generate nonnormal distributed multivariate random vectors with mean=0, var=1 and  given correlations and coefficients of skewness
  and excess kurtosis. This is done with the method of Vale &amp; Morelli: The coefficients of the Fleishman transform Y = -c  + bX +cX^2 + dX^3 are computed.
  from given skewness gamma[1] = E(Y^3) and kurtosis gamma[2] = E(Y^4) - 3. A indermediate correlation matrix is computed from the desired correlation 
  matrix and the Fleishman coefficients. A singular value decomposition of the indermediate correlation matrix is performed and  a matrix of independend 
  normal random numbers is generated and transformed into correlated ones. Finally the Fleishman transform is applied to the columns of this data matrix. — FleishmanIC

Functions to generate nonnormal distributed multivariate random vectors with mean=0, var=1 and  given correlations and coefficients of skewness
  and excess kurtosis. This is done with the method of Vale &amp; Morelli: The coefficients of the Fleishman transform Y = -c  + bX +cX^2 + dX^3 are computed.
  from given skewness gamma[1] = E(Y^3) and kurtosis gamma[2] = E(Y^4) - 3. A indermediate correlation matrix is computed from the desired correlation 
  matrix and the Fleishman coefficients. A singular value decomposition of the indermediate correlation matrix is performed and  a matrix of independend 
  normal random numbers is generated and transformed into correlated ones. Finally the Fleishman transform is applied to the columns of this data matrix.

Description

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Examples