rav: Analyzing the Family of the Averaging Models

Description

rav (R-Average for AVeraging models) is a procedure for estimating the parameters of the averaging models of Information Integration Theory (Anderson, 1981). It provides reliable estimations of weights and scale values for a factorial experimental design (with any number of factors and levels) by selecting the most suitable subset of the parameters, according to the overall goodness of fit indexes and to the complexity of the design. Its attributes can be handled by menas of a GUI (see the rav.cmd command for details).

Usage

rav(data, subset = NULL, lev, all= FALSE, sim = 0,
    start = NULL, lower = NULL, upper = NULL,
    I0 = FALSE, s.fixed = FALSE, w.fixed = FALSE,
    IC.diff = c(2.5, 2.0), delta.weights = 0.1,
    method = "L-BFGS-B", control = list(),
    title = NULL, names = NULL, verbose = FALSE)

Arguments

data

A matrix or a data.frame object containing the experimental data. Each column corresponds to an experimental design (in order: one-way design, two-way design, ..., full factorial design; see the example for furt

subset

Character, numeric or factor attribute that selects a subset of experimental data for the analysis (see the examples).

lev

Vector containing the number of levels of each factor. For instance, two factors with respectively 3 and 4 levels require lev = c(3,4).

all

Logical. If set TRUE the information criterion tests all the possible combinations of weights (see details). The default value FALSE implies a preselection of a subset of combination based on the results of the

sim

Number of iterations for the Monte-Carlo simulation procedure. The default setting 0 implies that no Monte-Carlo will be runned.

start

Vector containing the start scale and weight values, according to the following order: s0, w0, s(k,j), w(k,j), for k and j set by the factorial design. With the default setting NULL,

lower

Vector containing the lower scale and weight values, according to the following order: s0, w0, s(k,j), w(k,j), for k and j set by the factorial design. With the default setting NULL,

upper

Vector containing the upper scale and weight values, according to the following order: s0, w0, s(k,j), w(k,j), for k and j set by the factorial design. With the default setting NULL,

Logical. If set FALSE, the s0 and w0 parameters are forced to be zero. If set TRUE, the s0 and w0 parameters are free to be estimated.

s.fixed

Logical. Default setting to FALSE indicates that the scale values parameters are estimated by the algorithmic procedure. Otherwise, their values are fixedto the mean values of the one-way sub-designs (strongly suggested for

w.fixed

List or logical attribute. Can be used to set fixed values for the weight parameters. See the examples for further details. If set TRUE the procedure opens a pop-up that allows to fix the parameters without using a list obje

IC.diff

Vector containing the cut-off values (of both BIC and AIC indexes) at which different models are considered equivalent. Default setting: BIC difference = 2.5, AIC difference = 2.0 (IC.diff = c(2.5, 2.0)).

delta.weights

Numeric attribute that set the cut-off value at which different weights must be considered equal.

method

The minimization algorithm that has to be used. Options are: "L-BFGS-B", "BFGS", "Nelder-Mead", "SANN", "CG". See optim documentation for further informations.

control

A list of control parameters. See optim documentation for further informations.

title

Character. Puts a title on the output.

names

Vector of character strings containing the names of the factors.

verbose

Logical. If set TRUE the function prints general informations for every step of the information criterion procedure.

Value

An object of class "rav". The method summary applied to the rav object prints all the fitted models. The functions fitted, residuals and parameters can be used to extract respectively fitted values R, the matrix of residuals and the set of parameter estimated.

Details

The rav function implements the R-Average procedure (Vidotto & Vicentini, 2007), for the estimation of the parameters of the Averaging Model. Three different cases are tested: EAM (Equal weights Averaging Model), DAM (Differential weights Averaging Model) and a model selected by means of an Information Criterion. The routine estimates the scale values and the weight parameters by minimizing the residual sum of squares of the model. The Information Criterion procedure starts from the EAM and, step by step, analyzes different combinations of weights, checking whether a new estimated model is better than the previous baseline (to set the criterion for AIC/BIC differences between models change the argument IC.diff). Finally, only the best model between EAM, DAM, and IC is shown.

References

Akaike, H. (1976). Canonical correlation analysis of time series and the use of an information criterion. In: R. K. Mehra & D. G. Lainotis (Eds.), System identification: Advances and case studies (pp. 52-107). New York: Academic Press. Anderson, N. H. (1981). Foundations of Information Integration Theory. New York: Academic Press. Anderson, N. H. (1982). Methods of Information Integration Theory. New York: Academic Press. Anderson, N. H. (1991). Contributions to information integration theory: volume 1: cognition. Lawrence Erlbaum Associates, Hillsdale, New Jersey. Anderson, N. H. (2007). Comment on article of Vidotto and Vicentini. Teorie & Modelli, Vol. 12 (1-2), 223-224. Byrd, R. H., Lu, P., Nocedal, J., & Zhu, C. (1995). A limited memory algorithm for bound constrained optimization. Journal Scientific Computing, 16, 1190-1208. Kuha, J. (2004). AIC and BIC: Comparisons of Assumptions and Performance. Sociological Methods & Research, 33 (2), 188-229. Nelder, J. A., & Mead, R. (1965). A Simplex Method for Function Minimization. The Computer Journal, 7, 308-313. Vidotto, G., Massidda, D., & Noventa, S. (2010). Averaging models: parameters estimation with the R-Average procedure. Psicologica, 31, 461-475. Vidotto, G. & Vicentini, M. (2007). A general method for parameter estimation of averaging models. Teorie & Modelli, Vol. 12 (1-2), 211-221.

Examples

Run this code

# --------------------------------------
# Example 1: 3x3 factorial design
# --------------------------------------
# The first column is filled with a sequence of NA values.
# data(fmdata1)
# fmdata1

# For a two factors design, the matrix data contains the one-way
# sub-design and the two-ways full factorial design observed data.
# Pay attention to the columns order:
# sub-design: A1, A2, A3, B1, B2, B3
# full factorial: A1B1, A1B2, A1B3, A2B1, A2B2, A2B3, A3B1, A3B2, A3B3
# Start the R-Average procedure:
# fm1 <- rav(fmdata1, lev=c(3,3))
# fm1 # print the best model selected
# summary(fm1) # print the fitted models

# To insert the factor names:
# fact.names <- c("Name of factor A", "Name of factor B")
# fm1 <- rav(fmdata1, lev=c(3,3), names = fact.names)

# To insert a output title:
# out.title <- c("Put your title here")
# fm1 <- rav(fmdata1, lev=c(3,3), title=out.title)

# To supervise the information criterion work flow:
# fm1 <- rav(fmdata1, lev=c(3,3), verbose=TRUE)

# To increase the number of iterations of the minimization routine:
# fm1 <- rav(fmdata1, lev=c(3,3), control=list(maxit=5000))

# To set a fixed value for weights:
# wfix <- list(A=c(NA,0.4,0.4), B=c(NA,NA,NA))
# wfix
# Warning: NA specify no-fixed weights
# fm1.fix <- rav(fmdata1, lev=c(3,3), w.fixed=wfix)
# Otherwise, it's possible to call a GUI:
# fm1.fix <- rav(fmdata1, lev=c(3,3), w.fixed=TRUE)

# rav can work without sub-designs. If any sub-design is not available,
# the corresponding column must be coded with NA values. For example:
# fmdata1[,1:3] <- NA
# fmdata1
# fmdata1 # the A sub-design is empty
# fm1.bis <- rav(fmdata1, lev=c(3,3), title="Sub-design A is empty")

# Using a subset of data:
# data(pasta)
# pasta
# Analyzing "subj.04" only:
# fact.names <- c("Price","Packaging")
# fm.subj04 <- rav(pasta, subset="subj.04", lev=c(3,3), names=fact.names)

# --------------------------------------
# Example 2: 3x5 factorial design
# --------------------------------------
# data(fmdata2)
# (Pay attention to the columns order)
# fmdata2
# fm2 <- rav(fmdata2, lev=c(3,5))
# Removing all the one-way sub-design:
# fmdata2[,1:8] <- NA
# fm2.bis <- rav(fmdata2, lev=c(3,5))

# --------------------------------------
# Example 3: 3x2x3 factorial design
# --------------------------------------
# data(fmdata3)
# (Pay attention to the columns order)
# fm3 <- rav(fmdata3, lev=c(3,2,3))
# Removing all the one-way design and the AxC sub-design:
# fmdata3[,1:8] <- NA # one-way designs
# fmdata3[,15:23] <- NA # AxC design
# fm3 <- rav(fmdata3, lev=c(3,2,3))

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