genloglin {MRCV} | R Documentation |
Model the Association Among Two or Three MRCVs
Description
The genloglin
function uses a generalized loglinear modeling approach to estimate the association among two or three MRCVs. Standard errors are adjusted using a second-order Rao-Scott approach.
Usage
genloglin(data, I, J, K = NULL, model, add.constant = 0.5, boot = TRUE,
B = 1999, B.max = B, print.status = TRUE)
Arguments
data |
A data frame containing the raw data where rows correspond to the individual item response vectors, and columns correspond to the binary items, W1, ..., WI, Y1, ..., YJ, and Z1, ..., ZK (in this order). |
I |
The number of items corresponding to row variable W. |
J |
The number of items corresponding to column variable Y. |
K |
The number of items corresponding to strata variable Z. |
model |
For the two MRCV case, a character string specifying one of the following models: |
add.constant |
A positive constant to be added to all zero marginal cell counts. |
boot |
A logical value indicating whether bootstrap resamples should be taken. |
B |
The desired number of bootstrap resamples. |
B.max |
The maximum number of bootstrap resamples. Resamples for which at least one item has all positive or negative responses are thrown out; |
print.status |
A logical value indicating whether progress updates should be provided. When |
Details
The genloglin
function first converts the raw data into a form that can be used for estimation. For the two MRCV case, the reformatted data frame contains 2Ix2J rows and 5 columns generically named W
, Y
, wi
, yj
, and count
. For the three MRCV case, the reformatted data frame contains 2Ix2Jx2K rows and 7 columns generically named W
, Y
, Z
, wi
, yj
, zk
, and count
. Then, the model of interest is estimated by calling the glm
function where the family
argument is specified as poisson
. For all predictor variables, the first level is the reference group (i.e., 1 is the reference for variables W
, Y
, and Z
, and 0 is the reference for variables wi
, yj
, and zj
).
The boot
argument must equal TRUE
in order to obtain bootstrap results with the genloglin
method functions.
Value
— genloglin
returns an object of class 'genloglin'
. The object is a list containing at least the following objects: original.arg
, mod.fit
, sum.fit
, and rs.results
.
original.arg
is a list containing the following objects:
data
: The original data frame supplied to thedata
argument.I
: The original value supplied to theI
argument.J
: The original value supplied to theJ
argument.K
: The original value supplied to theK
argument.nvars
: The number of MRCVs.model
: The original value supplied to themodel
argument.add.constant
: The original value supplied to theadd.constant
argument.boot
: The original value supplied to theboot
argument.
mod.fit
is a list containing the same objects returned by glm
with a few modifications as described in summary.genloglin
.
sum.fit
is a list containing the same objects returned by the summary
method for class "glm"
with a few modifications as described in summary.genloglin
.
rs.results
is a list containing the following objects (see Appendix A of Bilder and Loughin, 2007, for more detail):
cov.mu
: The covariance matrix for the estimated cell counts.E
: The covariance matrix for the residuals.gamma
: Eigenvalues used in computing second-order Rao-Scott adjusted statistics.
— For boot = TRUE
, the primary list additionally includes boot.results
, a list containing the following objects:
B.use
: The number of bootstrap resamples used.B.discard
: The number of bootstrap resamples discarded due to having at least one item with all positive or negative responses.model.data.star
: For the two MRCV case, a numeric matrix containing 2Ix2J rows andB.use
+4 columns, where the first 4 columns correspond to the model variablesW
,Y
,wi
, andyj
, and the lastB.use
columns correspond to the observed counts for each resample. For the three MRCV case, a numeric matrix containing 2Ix2Jx2K rows andB.use+6
columns, where the first 6 columns correspond to the model variablesW
,Y
,Z
,wi
,yj
, andzk
, and the lastB.use
columns correspond to the observed counts for each resample.mod.fit.star
: For the two MRCV case, a numeric matrix containingB.use
rows and 2Ix2J +1 columns, where the first 2Ix2J columns correspond to the model-predicted counts for each resample, and the last column corresponds to the residual deviance for each resample. For the three MRCV case, a numeric matrix containingB.use
rows and 2Ix2Jx2K+1 columns, where the first 2Ix2Jx2K columns correspond to the model-predicted counts for each resample, and the last column corresponds to the residual deviance for each resample.chisq.star
: A numeric vector of lengthB.use
containing the Pearson statistics (comparingmodel
to the saturated model) calculated for each resample.lrt.star
: A numeric vector of lengthB.use
containing the LRT statistics calculated for each resample.residual.star
: A numeric matrix with 2Ix2J rows (or 2Ix2Jx2K rows for the three MRCV case) andB.use
columns containing the residuals calculated for each resample.
References
Bilder, C. and Loughin, T. (2007) Modeling association between two or more categorical variables that allow for multiple category choices. Communications in Statistics–Theory and Methods, 36, 433–451.
See Also
The genloglin
methods summary.genloglin
, residuals.genloglin
, anova.genloglin
, and predict.genloglin
, and the corresponding generic functions summary
, residuals
, anova
, and predict
.
The glm
function for fitting generalized linear models.
The MI.test
function for testing for MMI (one MRCV case) or SPMI (two MRCV case).
Examples
# Estimate the y-main effects model for 2 MRCVs
mod.fit <- genloglin(data = farmer2, I = 3, J = 4, model = "y.main", boot = FALSE)
# Summarize model fit information
summary(mod.fit)
# Examine standardized Pearson residuals
residuals(mod.fit)
# Compare the y-main effects model to the saturated model
anova(mod.fit, model.HA = "saturated", type = "rs2")
# Obtain observed and model-predicted odds ratios
predict(mod.fit)
# Estimate a model that is not one of the named models
# Note that this was the final model chosen by Bilder and Loughin (2007)
mod.fit.other <- genloglin(data = farmer2, I = 3, J = 4, model = count ~ -1 + W:Y +
wi%in%W:Y + yj%in%W:Y + wi:yj + wi:yj%in%Y + wi:yj%in%W3:Y1, boot =
FALSE)
# Compare this model to the y-main effects model
anova(mod.fit, model.HA = count ~ -1 + W:Y + wi%in%W:Y + yj%in%W:Y + wi:yj +
wi:yj%in%Y + wi:yj%in%W3:Y1, type = "rs2", gof = TRUE)
# To obtain bootstrap results from the method functions the genloglin() boot
# argument must be specified as TRUE (the default)
# A small B is used for demonstration purposes; normally, a larger B should be used
mod.fit <- genloglin(data = farmer2, I = 3, J = 4, model = "y.main", boot = TRUE,
B = 99)
residuals(mod.fit)
anova(mod.fit, model.HA = "saturated", type = "all")
predict(mod.fit)
# Estimate a model for 3 MRCVs
mod.fit.three <- genloglin(data = farmer3, I = 3, J = 4, K = 5, model = count ~
-1 + W:Y:Z + wi%in%W:Y:Z + yj%in%W:Y:Z + zk%in%W:Y:Z + wi:yj +
wi:yj%in%Y + wi:yj%in%W + wi:yj%in%Y:W + yj:zk + yj:zk%in%Z +
yj:zk%in%Y + yj:zk%in%Z:Y, boot = TRUE, B = 99)
residuals(mod.fit.three)
anova(mod.fit.three, model.HA = "saturated", type = "all")
predict(mod.fit.three, pair = "WY")