matrixpls (version 0.4.0)

weight.pls: Partial Least Squares and other iterative two-stage weight algorithms

Description

Estimates a weight matrix using Partial Least Squares or a related algorithm.

Usage

weight.pls(S, model, W.mod, outerEstimators = NULL,
  innerEstimator = inner.path, ..., convCheck = convCheck.absolute,
  tol = 1e-05, iter = 100, validateInput = TRUE)

Arguments

S

Covariance matrix of the data.

model

There are two options for this argument: 1. lavaan script or lavaan parameter table, or 2. a list containing three matrices inner, reflective, and formative defining the free regression paths in the model.

W.mod

An optional numeric matrix representing the weight patter and starting weights (i.e. the how the indicators are combined to form the composite variables). If this argument is not specified, the weight patter is defined based on the relationships in the

outerEstimators

A function or a list of functions used for outer estimation. If the value of this parameter is a function, the same function is applied to all composites. If the value of the parameter is a list, the composite n is estimated with the estimato

innerEstimator

A function used for inner estimation. Setting this argument to null will use identity matrix as inner estimates and causes the algorithm to converge after the first iteration. This is useful when using

...

All other arguments are passed through to outerEstimators and innerEstimator.

convCheck

A function that takes the old and new weight matrices and returns a scalar that is compared against tol to check for convergence. The default function calculates the differences between each cell of old and new weights and returns the largest

tol

Decimal value indicating the tolerance criterion for the iterations.

iter

An integer indicating the maximum number of iterations.

validateInput

A boolean indicating whether the validity of the parameter values should be tested.

Value

• An object of class "matrixplsweights", which is a matrix containing the weights with the following attributes:
• iterations
  Number of iterations performed
• converged
  A boolean indicating if the algorithm converged
• history
  A data.frame containing the weights for each iteration

Details

weight.pls calculates indicator weights by calling the innerEstimator and outerEstimators iteratively until either the convergence criterion or maximum number of iterations is reached and provides the results in a matrix.

Model can be specified in the lavaan format or the native matrixpls format. The native model format is a list of three binary matrices, inner, reflective, and formative specifying the free parameters of a model: inner (l x l) specifies the regressions between composites, reflective (k x l) specifies the regressions of observed data on composites, and formative (l x k) specifies the regressions of composites on the observed data. Here k is the number of observed variables and l is the number of composites.

If the model is specified in lavaan format, the native format model is derived from this model by assigning all regressions between latent variables to inner, all factor loadings to reflective, and all regressions of latent variables on observed variables to formative. Regressions between observed variables and all free covariances are ignored. All parameters that are specified in the model will be treated as free parameters. If model is specified in lavaan syntax, the model that is passed to the parameterEstimator will be that model and not the native format model.

The original papers about Partial Least Squares, as well as many of the current PLS implementations, impose restrictions on the matrices inner, reflective, and formative: inner must be a lower triangular matrix, reflective must have exactly one non-zero value on each row and must have at least one non-zero value on each column, and formative must only contain zeros. Some PLS implementations allow formative to contain non-zero values, but impose a restriction that the sum of reflective and t(formative) must satisfy the original restrictions of reflective. The only restrictions that matrixpls imposes on inner, reflective, and formative is that these must be binary matrices and that the diagonal of inner must be zeros.

The argument W.mod is a (l x k) matrix that indicates how the indicators are combined to form the composites. The original papers about Partial Least Squares as well as all current PLS implementations define this as t(reflective) | formative, which means that the weight patter must match the model specified in reflective and formative. Matrixpls does not require that W.mod needs to match reflective and formative, but accepts any numeric matrix. If this argument is not specified, W.mod is defined as t(reflective) | formative.

See Also

Inner estimators: inner.path; inner.centroid; inner.factor; inner.GSCA; inner.identity

Outer estimators: outer.modeA; outer.modeB; outer.GSCA; outer.factor; outer.fixedWeights

Convergence checks: convCheck.absolute, convCheck.square, and convCheck.relative.

Other Weight algorithms: weight.fixed; weight.optim