Package 'aspect'

Title: A General Framework for Multivariate Analysis with Optimal Scaling
Description: Contains various functions for optimal scaling. One function performs optimal scaling by maximizing an aspect (i.e. a target function such as the sum of eigenvalues, sum of squared correlations, squared multiple correlations, etc.) of the corresponding correlation matrix. Another function performs implements the LINEALS approach for optimal scaling by minimization of an aspect based on pairwise correlations and correlation ratios. The resulting correlation matrix and category scores can be used for further multivariate methods such as structural equation models.
Authors: Patrick Mair [cre, aut], Jan De Leeuw [aut]
Maintainer: Patrick Mair <[email protected]>
License: GPL-2
Version: 1.0-6
Built: 2024-12-11 19:24:14 UTC
Source: https://github.com/r-forge/psychor

Help Index

Scaling by Maximizing Correlational Aspects

Description

This function performs optimal scaling by maximizing a certain aspect of the correlation matrix.

Usage

corAspect(data, aspect = "aspectSum", level = "nominal", itmax = 100, eps = 1e-06, ...)

Arguments

data

Data frame or matrix
aspect

Function on the correlation matrix (see details)
level

Vector with scale level of the variables ("nominal" or "ordinal"). If all variables have the same scale level, only one value can be provided
itmax

Maximum number of iterations
eps

Convergence criterion
...

Additional parameters for aspect

Details

We provide various pre-specified aspects:

"aspectAbs" takes the sum of the absolute values of the correlations to the power pow. The optional argument pow = 1.

"aspectSum" the sum of the correlations to the power of pow. Again, as default pow = 1.

"aspectDeterminant" computes the determinant of the correlation matrix; no additional arguments needed.

"aspectEigen" the sum of the first p eigenvalues (principal component analysis). By default the argument p = 1.

"aspectSMC" the squared multiple correlations (multiple regression) with respect to a target variable. By default targvar = 1 which implies that the first variable of the dataset is taken as response.

"aspectSumSMC" uses the sum of all squared multiple correlations (path analysis).

Alternatively, the user can write his own aspect, e.g. the function myAspect(r, ...) with r as the correlation matrix. This function must return a list with the function value as first list element and the first derivative with respect to r as the second. Then aspect = myAspect and additional arguments go into ... in maxAspect().

Value

loss

Final value of the loss function
catscores

Resulting category scores (after optimal scaling)
cormat

Correlation matrix based on the scores
eigencor

Eigenvalues of the correlation matrix
indmat

Indicator matrix (dummy coded)
scoremat

Transformed data matrix (i.e with category scores resulting from optimal scaling)
burtmat

Burt matrix
niter

Number of iterations

Author(s)

Jan de Leeuw, Patrick Mair

References

Mair, P., & De Leeuw, J. (2010). Scaling variables by optimizing correlational and non-correlational aspects in R. Journal of Statistical Software, 32(9), 1-23. doi:10.18637/jss.v032.i09

de Leeuw, J. (1988). Multivariate analysis with optimal scaling. In S. Das Gupta and J.K. Ghosh, Proceedings of the International Conference on Advances in Multivariate Statistical Analysis, pp. 127-160. Calcutta: Indian Statistical Institute.

See Also

lineals

Examples

## maximizes the first eigenvalue
data(galo)
res.eig1 <- corAspect(galo[,1:4], aspect = "aspectEigen")
res.eig1
summary(res.eig1)

## maximizes the first 2 eigenvalues
res.eig2 <- corAspect(galo[,1:4], aspect = "aspectEigen", p = 2)
res.eig2

## maximizes the absolute value of cubic correlations
res.abs3 <- corAspect(galo[,1:4], aspect = "aspectAbs", pow = 3)
res.abs3

## maximizes the sum of squared correlations
res.cor2 <- corAspect(galo[,1:4], aspect = "aspectSum", pow = 2)
res.cor2

## maximizes the determinant
res.det <- corAspect(galo[,1:4], aspect = "aspectDeterminant")
res.det

## maximizes SMC, IQ as target variable
res.smc <- corAspect(galo[,1:4], aspect = "aspectSMC", targvar = 2)
res.smc

## maximizes the sum of SMC
res.sumsmc <- corAspect(galo[,1:4], aspect = "aspectSumSMC")
res.sumsmc

Duncan dataset

Description

At 4 points in time the objects (n = 1204 adolescents) were asked to rate cigarette, marijuana, and alcohol consumption on a 5-point scale.

Usage

galo

Format

Data frame with marijuana (POT), cigarette (CIG), and alcohol (ALC) consumption.

Category labels:

1 ... never consumed

2 ... previous but no use over the last 6 months

3 ... current use of less than 4 times a month

4 ... current use of between 4 and 29 times a month

5 ... current use of 30 or more times a month

References

Duncan, S. C., Duncan, T. E., and Hops, H. (1998). Progressions of alcohol, cigarette, and marijuana use in adolescence. Journal of Bahavioral Medicine, 21, 375-388.

Examples

data(duncan)
   duncan

GALO dataset

Description

The objects (individuals) are 1290 school children in the sixth grade of elementary school in the city of Groningen (Netherlands) in 1959.

Usage

galo

Format

Data frame with the five variables Gender, IQ, Advice, SES (fathers occupation) and School. IQ (original range 60 to 144) has been categorized into 9 ordered categories and the schools are enumerated from 1 to 37.

SES:

LoWC = Lower white collar; MidWC = Middle white collar; Prof = Professional, Managers; Shop = Shopkeepers; Skil = Schooled labor; Unsk = Unskilled labor.

Advice:

Agr = Agricultural; Ext = Extended primary education; Gen = General; Grls = Secondary school for girls; Man = Manual, including housekeeping; None = No further education; Uni = Pre-University.

References

Peschar, J.L. (1975). School, Milieu, Beroep. Groningen: Tjeek Willink.

Examples

data(galo)
   galo

Linearizing bivariate regressions

Description

This function performs optimal scaling in order to achieve linearizing transformations for each bivariate regression.

Usage

lineals(data, level = "nominal", itmax = 100, eps = 1e-06)

Arguments

data

Data frame or matrix
level

Vector with scale level of the variables ("nominal" or "ordinal"). If all variables have the same scale level, only one value can be provided
itmax

Maximum number of iterations
eps

Convergence criterion

Details

This function can be used as a preprocessing tool for categorical and ordinal data for subsequent factor analytical techniques such as structural equation models (SEM) using the resulting correlation matrix based on the transformed data. The estimates of the corresponding structural parameters are consistent if all bivariate regressions can be linearized.

Value

loss

Final value of the loss function
catscores

Resulting category scores (after optimal scaling)
cormat

Correlation matrix based on the scores
cor.rat

Matrix with correlation ratios
indmat

Indicator matrix (dummy coded)
scoremat

Transformed data matrix (i.e with category scores resulting from optimal scaling)
burtmat

Burt matrix
niter

Number of iterations

Author(s)

Jan de Leeuw, Patrick Mair

References

Mair, P., & De Leeuw, J. (2008). Scaling variables by optimizing correlational and non-correlational aspects in R. Journal of Statistical Software, 32(9), 1-23. doi:10.18637/jss.v032.i09

de Leeuw, J. (1988). Multivariate analysis with linearizable regressions. Psychometrika, 53, 437-454.

See Also

corAspect

Examples

data(galo)
res.lin <- lineals(galo)
summary(res.lin)

Plot method for aspect solutions

Description

This method provides regression plots and transformation plots for objects of class "aspect", i.e. solutions of corAspect and lineals

Usage

## S3 method for class 'aspect'
plot(x, plot.type, plot.var = c(1,2), xlab, ylab, main, type, ...)

Arguments

x

Object of class "aspect".
plot.type

Type of plot to be produced (details see below): "regplot", "transplot".
plot.var

For plot.type = "regplot" only. Vector of length 2 with variables to be plotted. Either variable names of column number.
xlab

Label x-axis.
ylab

Label y-axis.
main

Plot title.
type

Whether points, lines or both should be plotted.
...

Additional graphical parameters.

Details

The regression plot ("regplot") provides two plots. First, the unscaled solution is plotted. A frequency grid for the categories of the first variable (var1; x-axis) and the categories of the second variable (var2; y-axis) is produced. The regression line is based on the category weighted means of the relative frequencies: the blue line on the var1 means on the x-axis and the var2 categories on the y-axis, the red line is based on the var1 categories on the x-axis and the var2 means on the y-axis. In a second device the scaled solution is plotted. The frequency grid is determined by the var1 scores (x-axis) and the var2 scores(y-axis). Now, instead of the var1/var2 categories, the var1 scores (blue line y-axis) and the row scores (red line x-axis) are used.

The transformation plot ("transplot") plots the raw categories against the computed scores.

See Also

lineals, corAspect

Examples

##Regression plots using galo data
data(galo)
res <- lineals(galo[,1:4])
#plot(res, plot.type = "regplot", plot.var = c("advice","SES"))
#plot(res, plot.type = "transplot")

Internet terminals

Description

The dataset is about the use of public Internet terminals. For this package we extracted a subset of 8 items.

Usage

wurzer

Format

A data frame (n = 215) with the following items:

Do you know at least one place where you can finnd such a terminal? (yes/no)

Have you already used such a terminal? (yes/no)

How often do you use the Internet on each of the following locations: home, work, cafe, terminal, cellphone? (5-point scales; see below)

Which of the following descriptions fits you best? (I'm here on vacation/I am from here/I'm here on business travel)

The 5-point items we have the following categories: daily (1), almost daily (2), several times a week (3), several times a month (3), once a month (4), less frequently (5).

References

Wurzer, M. (2006). An Application of Configural Frequency Analysis: Evaluation of the Usage of Internet Terminals. Master's thesis, University of Vienna, Austria.

Examples

data(wurzer)
   wurzer