Quality Indices and Goodness of fit measures for pls path models

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Description

A collection of method to validate the goodness of the model. Since there is no well identified global optimization criterion each part of the model needs to be validated.

Usage

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rSquared(object, ...)
## S3 method for class 'sempls'
rSquared(object, na.rm=FALSE, ...)
## S3 method for class 'rSquared'
print(x, na.print=".", digits=2, ...)

qSquared(object, ...)
## S3 method for class 'sempls'
qSquared(object, d=NULL, impfun, dlines=TRUE,
         total=FALSE, ...)
## S3 method for class 'qSquared'
print(x, na.print=".", digits=2, ...)

dgrho(object, ...)
## S3 method for class 'sempls'
dgrho(object, ...)
## S3 method for class 'dgrho'
print(x, na.print=".", digits=2, ...)

communality(object, ...)
## S3 method for class 'sempls'
communality(object, ...)
## S3 method for class 'communality'
print(x, na.print=".", digits=2, ...)

redundancy(object, ...)
## S3 method for class 'sempls'
redundancy(object, ...)
## S3 method for class 'redundancy'
print(x, na.print=".", digits=2, ...)

rSquared2(object, ...)
## S3 method for class 'sempls'
rSquared2(object, na.rm=FALSE, ...)
## S3 method for class 'rSquared2'
print(x, na.print=".", digits=2, ...)

gof(object, ...)
## S3 method for class 'sempls'
gof(object, ...)
## S3 method for class 'gof'
print(x, na.print=".", digits=2, ...)

Arguments

object

An object of class sempls.

d

A numeric value for the omission distance. Thus choosing d=N, where N is the number of complete observations, is leaving one out cross validation. This is done when d takes its default value NULL.

impfun

An user specified function to impute missing values.

dlines

If TRUE the same observations are deleted for a whole block of MVs, else each dth , counting from top left to bottom right, observation is deleted.

total

If total=TRUE total effects are used instead of path coefficients to calculate the predictions.

na.rm

If na.rm=TRUE observation with missing values are discarded before analysis.

x

An object of the according class.

na.print

A character substituting values not to be printed.

digits

minimal number of _significant_ digits, see print.default.

...

Arguments to be passed down.

Value

Most GOF methods return a column vector with the names of the variables as rows and the respective measure as column.

References

Esposito Vinzi V., Trinchera L., Amato S. (2010). PLS Path Modeling: From Foundations to Recent Developments and Open Issues for Model Assessment and Improvement. In Esposito Vinzi V., Chin W.W., Henseler J., Wang H.F. (eds.), Handbook of Partial Least Squares: Concepts, Methods and Applications in Marketing and Related Fields, chapter 2. Springer-Verlag Berlin Heidelberg.

See Also

sempls, plsLoadings

Examples

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data(ECSImobi)
ecsi <- sempls(model=ECSImobi, data=mobi, E="C")

### R-squared
rSquared(ecsi)

### Q-squared with omission distance d=4
qSquared(ecsi, d=4)

### Dillon-Goldstein's rho (aka composite reliability)
dgrho(ecsi)

### Communalities
communality(ecsi)

### Redundancy
redundancy(ecsi)

### R-squared (normal + corrected)
rSquared2(ecsi)

### Goodness of fit
gof(ecsi)

### check for discriminant validity using loadings
l <-plsLoadings(ecsi)
print(l, type="discriminant", cutoff=0.5, reldiff=0.2)