aster (version 1.1-3)

foobar: Toy Life History Data having Directions of Recession

Description

Toy life history data created to exhibit the phenomenon of directions of recession. It was analyzed in a special topics course on aster models Fall 2018.

Usage

data(foobar)

Format

data(foobar) loads four R objects.

fam

a vector of family indices.

pred

a vector of predecessor indices.

vars

a vector of variable names associated with the nodes of the aster graph.

redata

a data frame having data on 300 individuals, each of which has length(vars) == 4 components of fitness, so the aster graph for one individual has four nodes. This data frame is already in long format; no need to reshape. The variables in this data frame are:

resp

the response vector.

varb

Categorical. Gives node of graphical model corresponding to each component of resp. See details below.

root

All ones. Root variables for graphical model.

id

Categorical. Individual ID numbers.

trt

Categorical. Treatment.

blk

Categorical. Block.

fit

Bernoulli (zero-or-one-valued). Indicator variable of the fitness nodes of the graph; in these data there is just one node for fitness.

Details

The levels of varb indicate nodes of the graphical model to which the corresponding elements of the response vector resp belong. This is the typical “long” format produced by the R reshape function. For each individual, there are several response variables. All response variables are combined in one vector resp. The variable varb indicates which “original” variable the the corresponding component of the response vector was. The variable id indicates which individual the corresponding component of the response vector was.

References

These data are analyzed in deck 9 of the slides for a special topics course on aster models taught fall semester 2018 (http://www.stat.umn.edu/geyer/8931aster/slides/s9.pdf).

Examples

data(foobar)
library(aster)
aout <- aster(resp ~ varb + fit : (trt * blk), pred,
    fam, varb, id, root, data = redata)
foo <- try(summary(aout))
# gives an error about directions of recession
# get directions of recession
dor <- attr(foo, "condition")$dor
dor
# found one apparent direction of recession
# from regular pattern
# it looks like a true direction of recession
dor <- dor / max(abs(dor))
dor
# but what does it do?  For that need to map to saturated model
# parameter space
modmat <- aout$modmat
dim(modmat)
# oof!  modmat is three-dimensional.  Need an actual matrix here.
modmat <- matrix(as.vector(modmat), ncol = length(dor))
dor.phi <- drop(modmat %*% dor)
names(dor.phi) <- with(redata, paste(id, as.character(varb), sep = "."))
dor.phi[dor.phi != 0]
fam.default()[fam[vars == "seeds"]]
# since the support of the Poisson distribution is bounded above,
# actually this must be minus the DOR (if it is a DOR at all).
# check that all components of response vector for which dor.phi == 1 are zero
# (lower bound of Poisson range)
all(redata$resp[dor.phi == 1] == 0)
# so minus dor.phi is a true direction of recession in the saturated model
# canonical parameter space, and minus dor is a true direction of recession
# in the submodel canonical parameter space
#
# try to get more info
trt.blk <- with(redata,
    paste(as.character(trt), as.character(blk), sep = "."))
unique(trt.blk[dor.phi == 1])
# the reason for the direction of recession is that every individual getting
# treatment a in block A had zero seeds.
#
# the reason the submodel DOR, R object dor, was so hard to interpret was
# because fit:trta:blkA is not in the model.  So let's force it in
redata <- transform(redata, trt = relevel(trt, ref = "b"),
    blk = relevel(blk, ref = "B"))
# Note: following code is copied exactly from above.  Only difference
# is releveling in the immediately preceding statement
aout <- aster(resp ~ varb + fit : (trt * blk), pred,
    fam, varb, id, root, data = redata)
foo <- try(summary(aout))
dor <- attr(foo, "condition")$dor
dor <- dor / max(abs(dor))
dor
# now it is obvious from looking at this dor that all individuals in trt a
# and blk A are at the lower end (zero) of the Poisson range.
# maybe the other dor we had previously would be "obvious" to someone
# sufficiently skilled in understanding the meaning of regression coefficients
# but not "obvious" to your humble author
#
# as for what to do about this, see the course slides cited in the reference
# section.  There is no single Right Thing to do.