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Effects of non-homogenous data loss

Table of Contents

1 General Information

The simulations described in Barr, Levy, Scheepers, and Tily assume only a small amount of missing data (<5%) missing at random. For some research applications, this may be overly optimistic. We therefore conducted simulations to assess the effect of larger proportions of missing data (10-80%), with an uneven distribution of missing data over subjects ("by subj"), conditions ("by cond"), or condition-by-subject combinations ("by subjcond"). We assess the overall Type I error rates and power for the three different scenarios, and also report the percent change in Type I error rate and power from the original, optimistic (<5%, homogeneous data loss) scenario.

2 Overall results

This first section reports results for that main analyses that do not use model selection. Note that we are only considering those approaches that had reasonable Type I error rates for the original simulations: \(F_1+F_2\), min-\(F'\), and maximal LMEMs with \(p\)-values derived through model comparison. The percent changes in Type I error rate and power are relative to the original, smaller <5% data loss scenario. (The original values are in the column labeled "Main" in the tables; negative percent change indicates more conservative performance).

2.1 Type I Error

MethodDesignNo.ItemMainSubjCondSubjCond%Subj%Cond%SubjCond
F1+F2wsbi12.06278.06382.05507.063761.7-12.31.6
min-F'wsbi12.04446.04134.03520.04140-7.0-2.8-6.9
LMEM, Maximal (LR)wsbi12.07026.07010.06928.07018-.2-1.4-.1
F1+F2wswi12.05742.04931.04492.04790-14.1-21.8-16.6
min-F'wswi12.02713.02178.01932.02025-19.7-28.8-25.4
LMEM, Maximal (LR)wswi12.05885.05904.05853.05795.3-.5-1.5
F1+F2wsbi24.07721.07824.06761.080621.3-12.44.4
min-F'wsbi24.04456.04307.03693.04418-3.3-17.1-.9
LMEM, Maximal (LR)wsbi24.05750.05863.05848.059102.01.72.8
F1+F2wswi24.07244.06707.05901.06371-7.4-18.5-12.1
min-F'wswi24.03070.02656.02237.02576-13.5-27.1-16.1
LMEM, Maximal (LR)wswi24.05594.05574.05676.05651-.41.51.0

2.2 Power

MethodDesignNo.ItemMainSubjCondSubjCond%Subj%Cond%SubjCond
F1+F2wsbi12.25183.22962.20708.22683-8.8-17.8-9.9
min-F'wsbi12.20992.17884.15855.17357-14.8-24.5-17.3
LMEM, Maximal (LR)wsbi12.26725.2518.24806.25001-5.8-7.2-6.5
F1+F2wswi12.43998.34422.31782.33477-21.8-27.8-23.9
min-F'wswi12.32682.23220.20998.22451-29.0-35.8-31.3
LMEM, Maximal (LR)wswi12.46032.41111.39766.40887-1.7-13.6-11.2
F1+F2wsbi24.40341.38207.35320.37629-5.3-12.4-6.7
min-F'wsbi24.32811.29519.26761.28915-10.0-18.4-11.9
LMEM, Maximal (LR)wsbi24.36361.34842.34541.34801-4.2-5.0-4.3
F1+F2wswi24.64318.55921.52955.54112-13.1-17.7-15.9
min-F'wswi24.51157.41622.38499.40282-18.6-24.7-21.3
LMEM, Maximal (LR)wswi24.61037.57046.56220.56699-6.5-7.9-7.1

3 Model selection

In this section, we compare the effects of non-homogeneous data loss on model selection techniques to its effects on maximal models. Each colored line in each graph represents a given model selection technique, with the horizontal axis indicating the specified \(\alpha\) level at which random slopes were tested. The two letter code in the legend for the within-items plot indicates the model selection technique, as follows:

CodeModel Selection Algorithm
BBBackward, Best Path
BIBackward, Test Item Slope before Subject Slope
BSBackward, Test Subject Slope before Item Slope
FBForward, Best Path
FIForward, Test Item Slope before Subject Slope
FSForward, Test Subject Slope before Item Slope

The numbers "12" and "24" preceding the codes in the legend indicate the number of items. See the main manuscript for more information about model selection algorithms. The dotted lines in the background reflect the performance of maximal models (one line for the 12-item datasets, and one for the 24-item datasets).

3.1 Between-items design

main (<5%)
by subj
by subj %chg
by cond
by cond %chg
by subjcond
by subjcond %chg

3.2 Within-items design

main (<5%)
by subj
by subj %chg
by cond
by cond %chg
by subjcond
by subjcond %chg

4 Discussion

The results from these simulations are very clear: maximal models are more robust against non-homogeneous data loss than separate \(F_1+F_2\) analyses, min-\(F'\) or model selection approaches. Unlike maximal models, all model selection approaches showed an increase in Type I error rate over all missing data scenarios, even approaching a 40% increase in some cases. The increase in Type I error rate for maximal models, in contrast, was negligible (<3%, at worst).

Maximal models showed less of a decrement in power relative to \(F_1+F_2\) or min-\(F'\), with the decrement ranging between 1.7% at best (by subj, within-items design, 12 items), and 13.6% at worst (by cond, within-items design, 12 items). Model selection approaches, once corrected for anticonservativity, never exceeded the power of maximal models.

The poor performance of model selection approaches in terms of Type I error may be explained by the fact that the missing data make it more difficult to detect the existence of random slope variance, increasing the likelihood that the slope will be excluded from the model.

5 R scripts

5.1 Between-items design

library(simgen)

mf <- modSpace(TRUE)[2:1]
param.mx <- createParamMx(nexp=100000)   # or load(file="param.RData")
nruns <- nrow(param.mx)

param.mx[,"eff"] <- 0

mcRun("fitstepwise", "newmselect/fitstepwise.h0.wsbi.12.MS.RData",
      "mkDf",
      mcr.constant=list(pMin=.1,pMax=.8),
      mcr.varying=param.mx[1:nruns,], mf=mf, nitem=12, wsbi=TRUE,
      missMeth="random")

mcRun("fitstepwise", "newmselect/fitstepwise.h0.wsbi.24.MS.RData",
      "mkDf",
      mcr.constant=list(pMin=.1,pMax=.8),
      mcr.varying=param.mx[1:nruns,], mf=mf, nitem=24, wsbi=TRUE,
      missMeth="random")

mcRun("fitstepwise", "missbysubj/fitstepwise.h0.wsbi.12.MS.RData",
      "mkDf",
      mcr.constant=list(pMin=.1,pMax=.8),
      mcr.varying=param.mx[1:nruns,], mf=mf, nitem=12, wsbi=TRUE,
      missMeth="bysubj")

mcRun("fitstepwise", "missbysubj/fitstepwise.h0.wsbi.24.MS.RData",
      "mkDf",
      mcr.constant=list(pMin=.1,pMax=.8),
      mcr.varying=param.mx[1:nruns,], mf=mf, nitem=24, wsbi=TRUE,
      missMeth="bysubj")

mcRun("fitstepwise", "missbycond/fitstepwise.h0.wsbi.12.MS.RData",
      "mkDf",
      mcr.constant=list(pMin=.1,pMax=.8),
      mcr.varying=param.mx[1:nruns,], mf=mf, nitem=12, wsbi=TRUE,
      missMeth="bycond")

mcRun("fitstepwise", "missbycond/fitstepwise.h0.wsbi.24.MS.RData",
      "mkDf",
      mcr.constant=list(pMin=.1,pMax=.8),
      mcr.varying=param.mx[1:nruns,], mf=mf, nitem=24, wsbi=TRUE,
      missMeth="bycond")

mcRun("fitstepwise", "missbysubjcond/fitstepwise.h0.wsbi.12.MS.RData",
      "mkDf",
      mcr.constant=list(pMin=.1,pMax=.8),
      mcr.varying=param.mx[1:nruns,], mf=mf, nitem=12, wsbi=TRUE,
      missMeth="bysubjcond")

mcRun("fitstepwise", "missbysubjcond/fitstepwise.h0.wsbi.24.MS.RData",
      "mkDf",
      mcr.constant=list(pMin=.1,pMax=.8),
      mcr.varying=param.mx[1:nruns,], mf=mf, nitem=24, wsbi=TRUE,
      missMeth="bysubjcond")

param.mx[,"eff"] <- .8

mcRun("fitstepwise", "newmselect/fitstepwise.h1.wsbi.12.MS.RData",
      "mkDf",
      mcr.constant=list(pMin=.1,pMax=.8),
      mcr.varying=param.mx[1:nruns,], mf=mf, nitem=12, wsbi=TRUE,
      missMeth="random")

mcRun("fitstepwise", "newmselect/fitstepwise.h1.wsbi.24.MS.RData",
      "mkDf",
      mcr.constant=list(pMin=.1,pMax=.8),
      mcr.varying=param.mx[1:nruns,], mf=mf, nitem=24, wsbi=TRUE,
      missMeth="random")

mcRun("fitstepwise", "missbysubj/fitstepwise.h1.wsbi.12.MS.RData",
      "mkDf",
      mcr.constant=list(pMin=.1,pMax=.8),
      mcr.varying=param.mx[1:nruns,], mf=mf, nitem=12, wsbi=TRUE,
      missMeth="bysubj")

mcRun("fitstepwise", "missbysubj/fitstepwise.h1.wsbi.24.MS.RData",
      "mkDf",
      mcr.constant=list(pMin=.1,pMax=.8),
      mcr.varying=param.mx[1:nruns,], mf=mf, nitem=24, wsbi=TRUE,
      missMeth="bysubj")

mcRun("fitstepwise", "missbycond/fitstepwise.h1.wsbi.12.MS.RData",
      "mkDf",
      mcr.constant=list(pMin=.1,pMax=.8),
      mcr.varying=param.mx[1:nruns,], mf=mf, nitem=12, wsbi=TRUE,
      missMeth="bycond")

mcRun("fitstepwise", "missbycond/fitstepwise.h1.wsbi.24.MS.RData",
      "mkDf",
      mcr.constant=list(pMin=.1,pMax=.8),
      mcr.varying=param.mx[1:nruns,], mf=mf, nitem=24, wsbi=TRUE,
      missMeth="bycond")

mcRun("fitstepwise", "missbysubjcond/fitstepwise.h1.wsbi.12.MS.RData",
      "mkDf",
      mcr.constant=list(pMin=.1,pMax=.8),
      mcr.varying=param.mx[1:nruns,], mf=mf, nitem=12, wsbi=TRUE,
      missMeth="bysubjcond")

mcRun("fitstepwise", "missbysubjcond/fitstepwise.h1.wsbi.24.MS.RData",
      "mkDf",
      mcr.constant=list(pMin=.1,pMax=.8),
      mcr.varying=param.mx[1:nruns,], mf=mf, nitem=24, wsbi=TRUE,
      missMeth="bysubjcond")

5.2 Within-items design

library(simgen)

mf <- modSpace(FALSE)
mf.sfirst <- c(mf[3], mf[[2]][1], mf[1])
mf.ifirst <- c(mf[3], mf[[2]][2], mf[1])

param.mx <- createParamMx(nexp=100000)   # or load(file="param.RData")
nruns <- nrow(param.mx)

param.mx[,"eff"] <- 0

# main (missing data < 5%)
mcRun("fitstepwise", "newmselect/fitstepwise.h0.wswi.12.FSBI.csv",
      "mkDf", mcr.constant=list(pMin=.1,pMax=.8), mcr.varying=param.mx[1:nruns,], 
      nitem=12, wsbi=FALSE, missMeth="random", mf=mf.sfirst)

mcRun("fitstepwise", "newmselect/fitstepwise.h0.wswi.24.FSBI.csv",
      "mkDf", mcr.constant=list(pMin=.1,pMax=.8), mcr.varying=param.mx[1:nruns,], 
      nitem=24, wsbi=FALSE, missMeth="random", mf=mf.sfirst)

mcRun("fitstepwise", "newmselect/fitstepwise.h0.wswi.12.FIBS.csv",
      "mkDf", mcr.constant=list(pMin=.1,pMax=.8), mcr.varying=param.mx[1:nruns,], 
      nitem=12, wsbi=FALSE, missMeth="random", mf=mf.ifirst)

mcRun("fitstepwise", "newmselect/fitstepwise.h0.wswi.24.FIBS.csv",
      "mkDf", mcr.constant=list(pMin=.1,pMax=.8), mcr.varying=param.mx[1:nruns,], 
      nitem=24, wsbi=FALSE, missMeth="random", mf=mf.ifirst)

mcRun("fitstepwise.bestpath", "newmselect/fitstepwise.h0.wswi.24.FB.csv",
      "mkDf", mcr.constant=list(pMin=.1,pMax=.8), mcr.varying=param.mx[1:nruns,], 
      nitem=24, wsbi=FALSE, missMeth="random", forward=TRUE)

mcRun("fitstepwise.bestpath", "newmselect/fitstepwise.h0.wswi.24.BB.csv",
      "mkDf", mcr.constant=list(pMin=.1,pMax=.8), mcr.varying=param.mx[1:nruns,], 
      nitem=24, wsbi=FALSE, missMeth="random", forward=FALSE)

# missing by subject
mcRun("fitstepwise", "missbysubj/fitstepwise.h0.wswi.12.FSBI.csv",
      "mkDf", mcr.constant=list(pMin=.1,pMax=.8), mcr.varying=param.mx[1:nruns,], 
      nitem=12, wsbi=FALSE, missMeth="bysubj", mf=mf.sfirst)

mcRun("fitstepwise", "missbysubj/fitstepwise.h0.wswi.24.FSBI.csv",
      "mkDf", mcr.constant=list(pMin=.1,pMax=.8), mcr.varying=param.mx[1:nruns,], 
      nitem=24, wsbi=FALSE, missMeth="bysubj", mf=mf.sfirst)

mcRun("fitstepwise", "missbysubj/fitstepwise.h0.wswi.12.FIBS.csv",
      "mkDf", mcr.constant=list(pMin=.1,pMax=.8), mcr.varying=param.mx[1:nruns,], 
      nitem=12, wsbi=FALSE, missMeth="bysubj", mf=mf.ifirst)

mcRun("fitstepwise", "missbysubj/fitstepwise.h0.wswi.24.FIBS.csv",
      "mkDf", mcr.constant=list(pMin=.1,pMax=.8), mcr.varying=param.mx[1:nruns,], 
      nitem=24, wsbi=FALSE, missMeth="bysubj", mf=mf.ifirst)

mcRun("fitstepwise.bestpath", "missbysubj/fitstepwise.h0.wswi.24.FB.csv",
      "mkDf", mcr.constant=list(pMin=.1,pMax=.8), mcr.varying=param.mx[1:nruns,], 
      nitem=24, wsbi=FALSE, missMeth="bysubj", forward=TRUE)

mcRun("fitstepwise.bestpath", "missbysubj/fitstepwise.h0.wswi.24.BB.csv",
      "mkDf", mcr.constant=list(pMin=.1,pMax=.8), mcr.varying=param.mx[1:nruns,], 
      nitem=24, wsbi=FALSE, missMeth="bysubj", forward=FALSE)

# missing by condition
mcRun("fitstepwise", "missbycond/fitstepwise.h0.wswi.12.FSBI.csv",
      "mkDf", mcr.constant=list(pMin=.1,pMax=.8), mcr.varying=param.mx[1:nruns,], 
      nitem=12, wsbi=FALSE, missMeth="bycond", mf=mf.sfirst)

mcRun("fitstepwise", "missbycond/fitstepwise.h0.wswi.24.FSBI.csv",
      "mkDf", mcr.constant=list(pMin=.1,pMax=.8), mcr.varying=param.mx[1:nruns,], 
      nitem=24, wsbi=FALSE, missMeth="bycond", mf=mf.sfirst)

mcRun("fitstepwise", "missbycond/fitstepwise.h0.wswi.12.FIBS.csv",
      "mkDf", mcr.constant=list(pMin=.1,pMax=.8), mcr.varying=param.mx[1:nruns,], 
      nitem=12, wsbi=FALSE, missMeth="bycond", mf=mf.ifirst)

mcRun("fitstepwise", "missbycond/fitstepwise.h0.wswi.24.FIBS.csv",
      "mkDf", mcr.constant=list(pMin=.1,pMax=.8), mcr.varying=param.mx[1:nruns,], 
      nitem=24, wsbi=FALSE, missMeth="bycond", mf=mf.ifirst)

mcRun("fitstepwise.bestpath", "missbycond/fitstepwise.h0.wswi.24.FB.csv",
      "mkDf", mcr.constant=list(pMin=.1,pMax=.8), mcr.varying=param.mx[1:nruns,], 
      nitem=24, wsbi=FALSE, missMeth="bycond", forward=TRUE)

mcRun("fitstepwise.bestpath", "missbycond/fitstepwise.h0.wswi.24.BB.csv",
      "mkDf", mcr.constant=list(pMin=.1,pMax=.8), mcr.varying=param.mx[1:nruns,], 
      nitem=24, wsbi=FALSE, missMeth="bycond", forward=FALSE)

# missing by subjcond
mcRun("fitstepwise", "missbysubjcond/fitstepwise.h0.wswi.12.FSBI.csv",
      "mkDf", mcr.constant=list(pMin=.1,pMax=.8), mcr.varying=param.mx[1:nruns,], 
      nitem=12, wsbi=FALSE, missMeth="bysubjcond", mf=mf.sfirst)

mcRun("fitstepwise", "missbysubjcond/fitstepwise.h0.wswi.24.FSBI.csv",
      "mkDf", mcr.constant=list(pMin=.1,pMax=.8), mcr.varying=param.mx[1:nruns,], 
      nitem=24, wsbi=FALSE, missMeth="bysubjcond", mf=mf.sfirst)

mcRun("fitstepwise", "missbysubjcond/fitstepwise.h0.wswi.12.FIBS.csv",
      "mkDf", mcr.constant=list(pMin=.1,pMax=.8), mcr.varying=param.mx[1:nruns,], 
      nitem=12, wsbi=FALSE, missMeth="bysubjcond", mf=mf.ifirst)

mcRun("fitstepwise", "missbysubjcond/fitstepwise.h0.wswi.24.FIBS.csv",
      "mkDf", mcr.constant=list(pMin=.1,pMax=.8), mcr.varying=param.mx[1:nruns,], 
      nitem=24, wsbi=FALSE, missMeth="bysubjcond", mf=mf.ifirst)

mcRun("fitstepwise.bestpath", "missbysubjcond/fitstepwise.h0.wswi.24.FB.csv",
      "mkDf", mcr.constant=list(pMin=.1,pMax=.8), mcr.varying=param.mx[1:nruns,], 
      nitem=24, wsbi=FALSE, missMeth="bysubjcond", forward=TRUE)

mcRun("fitstepwise.bestpath", "missbysubjcond/fitstepwise.h0.wswi.24.BB.csv",
      "mkDf", mcr.constant=list(pMin=.1,pMax=.8), mcr.varying=param.mx[1:nruns,], 
      nitem=24, wsbi=FALSE, missMeth="bysubjcond", forward=FALSE)

param.mx[,"eff"] <- .8

# main (missing data < 5%)
mcRun("fitstepwise", "newmselect/fitstepwise.h1.wswi.12.FSBI.csv",
      "mkDf", mcr.constant=list(pMin=.1,pMax=.8), mcr.varying=param.mx[1:nruns,], 
      nitem=12, wsbi=FALSE, missMeth="random", mf=mf.sfirst)

mcRun("fitstepwise", "newmselect/fitstepwise.h1.wswi.24.FSBI.csv",
      "mkDf", mcr.constant=list(pMin=.1,pMax=.8), mcr.varying=param.mx[1:nruns,], 
      nitem=24, wsbi=FALSE, missMeth="random", mf=mf.sfirst)

mcRun("fitstepwise", "newmselect/fitstepwise.h1.wswi.12.FIBS.csv",
      "mkDf", mcr.constant=list(pMin=.1,pMax=.8), mcr.varying=param.mx[1:nruns,], 
      nitem=12, wsbi=FALSE, missMeth="random", mf=mf.ifirst)

mcRun("fitstepwise", "newmselect/fitstepwise.h1.wswi.24.FIBS.csv",
      "mkDf", mcr.constant=list(pMin=.1,pMax=.8), mcr.varying=param.mx[1:nruns,], 
      nitem=24, wsbi=FALSE, missMeth="random", mf=mf.ifirst)

mcRun("fitstepwise.bestpath", "newmselect/fitstepwise.h1.wswi.24.FB.csv",
      "mkDf", mcr.constant=list(pMin=.1,pMax=.8), mcr.varying=param.mx[1:nruns,], 
      nitem=24, wsbi=FALSE, missMeth="random", forward=TRUE)

mcRun("fitstepwise.bestpath", "newmselect/fitstepwise.h1.wswi.24.BB.csv",
      "mkDf", mcr.constant=list(pMin=.1,pMax=.8), mcr.varying=param.mx[1:nruns,], 
      nitem=24, wsbi=FALSE, missMeth="random", forward=FALSE)

# missing by subject
mcRun("fitstepwise", "missbysubj/fitstepwise.h1.wswi.12.FSBI.csv",
      "mkDf", mcr.constant=list(pMin=.1,pMax=.8), mcr.varying=param.mx[1:nruns,], 
      nitem=12, wsbi=FALSE, missMeth="bysubj", mf=mf.sfirst)

mcRun("fitstepwise", "missbysubj/fitstepwise.h1.wswi.24.FSBI.csv",
      "mkDf", mcr.constant=list(pMin=.1,pMax=.8), mcr.varying=param.mx[1:nruns,], 
      nitem=24, wsbi=FALSE, missMeth="bysubj", mf=mf.sfirst)

mcRun("fitstepwise", "missbysubj/fitstepwise.h1.wswi.12.FIBS.csv",
      "mkDf", mcr.constant=list(pMin=.1,pMax=.8), mcr.varying=param.mx[1:nruns,], 
      nitem=12, wsbi=FALSE, missMeth="bysubj", mf=mf.ifirst)

mcRun("fitstepwise", "missbysubj/fitstepwise.h1.wswi.24.FIBS.csv",
      "mkDf", mcr.constant=list(pMin=.1,pMax=.8), mcr.varying=param.mx[1:nruns,], 
      nitem=24, wsbi=FALSE, missMeth="bysubj", mf=mf.ifirst)

mcRun("fitstepwise.bestpath", "missbysubj/fitstepwise.h1.wswi.24.FB.csv",
      "mkDf", mcr.constant=list(pMin=.1,pMax=.8), mcr.varying=param.mx[1:nruns,], 
      nitem=24, wsbi=FALSE, missMeth="bysubj", forward=TRUE)

mcRun("fitstepwise.bestpath", "missbysubj/fitstepwise.h1.wswi.24.BB.csv",
      "mkDf", mcr.constant=list(pMin=.1,pMax=.8), mcr.varying=param.mx[1:nruns,], 
      nitem=24, wsbi=FALSE, missMeth="bysubj", forward=FALSE)

# missing by condition
mcRun("fitstepwise", "missbycond/fitstepwise.h1.wswi.12.FSBI.csv",
      "mkDf", mcr.constant=list(pMin=.1,pMax=.8), mcr.varying=param.mx[1:nruns,], 
      nitem=12, wsbi=FALSE, missMeth="bycond", mf=mf.sfirst)

mcRun("fitstepwise", "missbycond/fitstepwise.h1.wswi.24.FSBI.csv",
      "mkDf", mcr.constant=list(pMin=.1,pMax=.8), mcr.varying=param.mx[1:nruns,], 
      nitem=24, wsbi=FALSE, missMeth="bycond", mf=mf.sfirst)

mcRun("fitstepwise", "missbycond/fitstepwise.h1.wswi.12.FIBS.csv",
      "mkDf", mcr.constant=list(pMin=.1,pMax=.8), mcr.varying=param.mx[1:nruns,], 
      nitem=12, wsbi=FALSE, missMeth="bycond", mf=mf.ifirst)

mcRun("fitstepwise", "missbycond/fitstepwise.h1.wswi.24.FIBS.csv",
      "mkDf", mcr.constant=list(pMin=.1,pMax=.8), mcr.varying=param.mx[1:nruns,], 
      nitem=24, wsbi=FALSE, missMeth="bycond", mf=mf.ifirst)

mcRun("fitstepwise.bestpath", "missbycond/fitstepwise.h1.wswi.24.FB.csv",
      "mkDf", mcr.constant=list(pMin=.1,pMax=.8), mcr.varying=param.mx[1:nruns,], 
      nitem=24, wsbi=FALSE, missMeth="bycond", forward=TRUE)

mcRun("fitstepwise.bestpath", "missbycond/fitstepwise.h1.wswi.24.BB.csv",
      "mkDf", mcr.constant=list(pMin=.1,pMax=.8), mcr.varying=param.mx[1:nruns,], 
      nitem=24, wsbi=FALSE, missMeth="bycond", forward=FALSE)

# missing by subjcond
mcRun("fitstepwise", "missbysubjcond/fitstepwise.h1.wswi.12.FSBI.csv",
      "mkDf", mcr.constant=list(pMin=.1,pMax=.8), mcr.varying=param.mx[1:nruns,], 
      nitem=12, wsbi=FALSE, missMeth="bysubjcond", mf=mf.sfirst)

mcRun("fitstepwise", "missbysubjcond/fitstepwise.h1.wswi.24.FSBI.csv",
      "mkDf", mcr.constant=list(pMin=.1,pMax=.8), mcr.varying=param.mx[1:nruns,], 
      nitem=24, wsbi=FALSE, missMeth="bysubjcond", mf=mf.sfirst)

mcRun("fitstepwise", "missbysubjcond/fitstepwise.h1.wswi.12.FIBS.csv",
      "mkDf", mcr.constant=list(pMin=.1,pMax=.8), mcr.varying=param.mx[1:nruns,], 
      nitem=12, wsbi=FALSE, missMeth="bysubjcond", mf=mf.ifirst)

mcRun("fitstepwise", "missbysubjcond/fitstepwise.h1.wswi.24.FIBS.csv",
      "mkDf", mcr.constant=list(pMin=.1,pMax=.8), mcr.varying=param.mx[1:nruns,], 
      nitem=24, wsbi=FALSE, missMeth="bysubjcond", mf=mf.ifirst)

mcRun("fitstepwise.bestpath", "missbysubjcond/fitstepwise.h1.wswi.24.FB.csv",
      "mkDf", mcr.constant=list(pMin=.1,pMax=.8), mcr.varying=param.mx[1:nruns,], 
      nitem=24, wsbi=FALSE, missMeth="bysubjcond", forward=TRUE)

mcRun("fitstepwise.bestpath", "missbysubjcond/fitstepwise.h1.wswi.24.BB.csv",
      "mkDf", mcr.constant=list(pMin=.1,pMax=.8), mcr.varying=param.mx[1:nruns,], 
      nitem=24, wsbi=FALSE, missMeth="bysubjcond", forward=FALSE)

Author: Dale J. Barr, Roger Levy, Christoph Scheepers, and Harry J. Tily (daleb@daleb-pc)

Date: March 27, 2012

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