matrixplsboot: Bootstrapping of matrixpls function

In matrixpls: Matrix-Based Partial Least Squares Estimation

Description

matrixpls.boot is a convenience method that implements bootstrapping of matrixpls with boot method of the boot package.

Usage

matrixpls.boot(
  data,
  model,
  ...,
  R = 500,
  signChange = NULL,
  parallel = c("no", "multicore", "snow"),
  ncpus = getOption("boot.ncpus", 1L),
  dropInadmissible = FALSE,
  stopOnError = FALSE,
  extraFun = NULL
)

## S3 method for class 'matrixplsboot'
summary(object, ..., ci.type = "all")

Arguments

data	Matrix or data frame containing the raw 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.
...	All other arguments are passed through to matrixpls and boot.
R	Number of bootstrap samples to draw.
signChange	Sign change correction function.
parallel	The type of parallel operation to be used (if any). If missing, the default is taken from the option "boot.parallel" (and if that is not set, "no").
ncpus	integer: number of processes to be used in parallel operation: typically one would chose this to the number of available CPUs.
dropInadmissible	A logical indicating whether non-convergent and inadmissible replications should be discarded.
stopOnError	A logical indicating whether boostrapping should be continued when error occurs in a replication.
extraFun	A function that takes a matrixpls object and a boostrap sample and returns a numeric vector. The vector is appended to bootstrap replication. Can be used for boostrapping additional statistics calculated based on the estimation results.
object	object of class matrixplsboot
ci.type	A vector of character strings representing the type of intervals required. Passed on to boot.ci. If "none", no confidence intervals are calculated.

Value

An object of class matrixplsboot and boot.

Analyzing the boostrap results

The output can be analyzed with any of the functions provided by the boot package. For example, the boot.ci function can be used for calculating confidence intervals and the empinf function can be used to calculate influence values that may be useful for identifying outliers.

The class matrixplsboot provides only a summary function, which calculates a set of statistics that are commonly of interest after boostrapping. This includes standard errors, t statistics (estimate / SE) and p-values based on Student's t distribution and standard normal distribution. Because the sampling distribution of the parameter estimates calculated by matrixpls are not always known, the p-values cannot be expected to be unbiased.

This concern applies particularly when using PLS weights. Because the PLS literature provides conflicting advice on which probability distribution to use as a reference, the summary method of matrixplsboot produces two-tailed p-values based on four different probability distributions. The regression p values are based on comparing the t statistic against the references distribution used in regression analysis, namely Student's t distribution with n - k - 1 degrees of freedom. The Hair p values are based on Hair et al's (2014, p. 134) recommendation to ignore the number of independent variables k and set the degrees of freedom to n - 1. The Henseler p values are based on the recommendation by Henseler et al (2009, p. 305) that the degrees of freedom should be set as n + m - 2, where mis always 1 and n is the number of bootstrap samples. The z p values are based on comparing the t statistic against the standard normal distribution. This choice can be motivated by asymptotic normality of the PLS estimates in certain conditions.

References

Hair, J. F., Hult, G. T. M., Ringle, C. M., & Sarstedt, M. (2014). A primer on partial least squares structural equations modeling (PLS-SEM). Los Angeles: SAGE.

Henseler, J., Ringle, C. M., & Sinkovics, R. R. (2009). The use of partial least squares path modeling in international marketing. Advances in International Marketing, 20, 277–319.

Rönkkö, M., & Evermann, J. (2013). A critical examination of common beliefs about partial least squares path modeling. Organizational Research Methods, 16(3), 425–448. doi: 10.1177/1094428112474693

Rönkkö, M., McIntosh, C. N., & Antonakis, J. (2015). On the adoption of partial least squares in psychological research: Caveat emptor. Personality and Individual Differences, (87), 76–84. doi: 10.1016/j.paid.2015.07.019

See Also

boot

Sign change corrections: signChange.individual; signChange.construct

Examples

# Run the customer satisfaction example form plspm

# load dataset satisfaction
data(satisfaction)
# inner model matrix
IMAG = c(0,0,0,0,0,0)
EXPE = c(1,0,0,0,0,0)
QUAL = c(0,1,0,0,0,0)
VAL = c(0,1,1,0,0,0)
SAT = c(1,1,1,1,0,0)
LOY = c(1,0,0,0,1,0)
inner = rbind(IMAG, EXPE, QUAL, VAL, SAT, LOY)
colnames(inner) <- rownames(inner)

# Reflective model

reflective<- matrix(
  c(1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
    0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0,
    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0,
    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1),
  27,6, dimnames = list(colnames(satisfaction)[1:27],colnames(inner)))

# empty formative model

formative <- matrix(0, 6, 27, dimnames = list(colnames(inner),
                                              colnames(satisfaction)[1:27]))

# Only 100 replications to make the example faster when running on single processor. 
# Increase the number of replications (e.g. to 500) to get the BCa intervals

matrixpls.boot.out <- matrixpls.boot(satisfaction[,1:27],
                           model = list(inner = inner,
                                        reflective = reflective,
                                        formative = formative),
                           R = 100)

print(matrixpls.boot.out)
summary(matrixpls.boot.out)

matrixpls documentation built on April 28, 2021, 5:07 p.m.