[R] Goodness of fit statistics for cfa are missing (sem package)
Simon Kiss
sjkiss at gmail.com
Tue Jul 9 19:28:22 CEST 2013
Dear colleagues,
I'm working on a confirmatory factor analysis and the model is not returning most of the usual goodness-of-fit statistics.
I'm testing whether this survey data confirms a hypothesized two-factor uncorrelated structure that has theoretical and empirical support from another case.
Below is (hopefully!) reproducible code which creates ff.cov a replica of the covariance matrix from my own data, the model that I have specified and am testing (cfa.mod.1) and the sem test of that model (cfa) and then a summary of the model fit (summary(cfa1)).
The problem is that many of the usual measures o goodness-of-fit do not appear after summary(cfa1). I only get a chi-square statistic, degrees of freedom and a BIC.
I saw a previous question on the R-mailing list that raised a similar issue and it was suggested that the problem lay in the specification of the model and that the degrees of freedom there were 0. Here, though, the df is 77. Unfortunately I can't find that question in the archives again or I would have linked to it.
The data set includes 376 observations and has 14 variables. Seven (coded with an h in the variable name, as in cc.h.varname.e or h) are hypothesized to load on one factor uncorrelated with the second factor, coded with a c (as in cc.c.varname.c or i).
I used this for guidance http://vimeo.com/38941937
Yours, Simon Kiss
#Load Libraries
library(sem)
#Create Covariance Matrix
ff.cov <-
structure(c(0.0925407885304659, 0.0296839426523298, 0.00787168458781362,
0.0261784946236559, 0.0031878853046595, 0.0261837275985663, 0.00847584229390681,
-0.00106, -0.00600867383512545, -0.010714623655914, -0.0123756272401434,
-0.00528007168458781, -0.00116, 0.000812186379928316, 0.0296839426523298,
0.0665810023041475, 0.00836764592933948, 0.0281491359447005,
0.00793406810035842, 0.0169870865335381, 0.00258921786994368,
0.000712720174091142, -0.00318649385560676, -0.0083643253968254,
-0.0133228366615463, -0.00557817844342038, -0.00224328341013825,
-0.000821018945212493, 0.00787168458781362, 0.00836764592933948,
0.0804340181771633, 0.00589630696364567, 0.0201758960573477,
0.012536866359447, 0.000343669994879673, 0.00425544674859191,
-0.00838453020993344, 0.00563975294418843, 0.00256180235535074,
0.00609073860727087, -0.00659535970302099, 0.00495727086533538,
0.0261784946236559, 0.0281491359447005, 0.00589630696364567,
0.0716310995903738, 0.00856442652329749, 0.0175328725038402,
0.0104401625704045, 0.0074095942140297, 0.00455983742959549,
-0.0123115783410138, -0.0192821300563236, -0.0166337109575013,
0.00623943292370712, -0.0114852790578597, 0.0031878853046595,
0.00793406810035842, 0.0201758960573477, 0.00856442652329749,
0.0550506451612903, 0.00998831541218638, -0.000462311827956989,
-0.0019576523297491, -0.0053855017921147, 0.00893281362007168,
8.10035842293904e-05, 0.00704324372759857, -0.00593381720430108,
-0.00112867383512545, 0.0261837275985663, 0.0169870865335381,
0.012536866359447, 0.0175328725038402, 0.00998831541218638, 0.050779846390169,
0.00705281105990783, -0.00306167946748592, -0.00736291858678955,
0.00135779825908858, -0.00280025601638505, 0.00161077316948285,
-0.00899035330261137, 0.00921536098310292, 0.00847584229390681,
0.00258921786994368, 0.000343669994879673, 0.0104401625704045,
-0.000462311827956989, 0.00705281105990783, 0.0475710074244752,
-0.0101174718381976, -0.0102886418330773, -0.0175483013312852,
-0.0107030209933436, -0.00982140168970814, -0.00959551843317972,
-0.00663934971838198, -0.00106, 0.000712720174091142, 0.00425544674859191,
0.0074095942140297, -0.0019576523297491, -0.00306167946748592,
-0.0101174718381976, 0.0572903110599078, 0.0148363965693804,
0.0134899987199181, 0.0172146441372248, 0.00366528545826933,
0.0148914759344598, 0.00469321556579621, -0.00600867383512545,
-0.00318649385560676, -0.00838453020993344, 0.00455983742959549,
-0.0053855017921147, -0.00736291858678955, -0.0102886418330773,
0.0148363965693804, 0.0650389644137225, 0.00571948412698413,
0.00671484895033282, -0.000752505120327701, 0.0295244790066564,
-0.00901979006656426, -0.010714623655914, -0.0083643253968254,
0.00563975294418843, -0.0123115783410138, 0.00893281362007168,
0.00135779825908858, -0.0175483013312852, 0.0134899987199181,
0.00571948412698413, 0.0839045558115719, 0.0463349206349206,
0.0350310253456221, 0.00760227470558116, 0.035818561187916, -0.0123756272401434,
-0.0133228366615463, 0.00256180235535074, -0.0192821300563236,
8.10035842293904e-05, -0.00280025601638505, -0.0107030209933436,
0.0172146441372248, 0.00671484895033282, 0.0463349206349206,
0.073641986687148, 0.0295747055811572, 0.00827306707629288, 0.0317729134664619,
-0.00528007168458781, -0.00557817844342038, 0.00609073860727087,
-0.0166337109575013, 0.00704324372759857, 0.00161077316948285,
-0.00982140168970814, 0.00366528545826933, -0.000752505120327701,
0.0350310253456221, 0.0295747055811572, 0.0607050576036866, 0.00305336789554532,
0.0243178443420379, -0.00116, -0.00224328341013825, -0.00659535970302099,
0.00623943292370712, -0.00593381720430108, -0.00899035330261137,
-0.00959551843317972, 0.0148914759344598, 0.0295244790066564,
0.00760227470558116, 0.00827306707629288, 0.00305336789554532,
0.0525731067588326, 0.000673143881208398, 0.000812186379928316,
-0.000821018945212493, 0.00495727086533538, -0.0114852790578597,
-0.00112867383512545, 0.00921536098310292, -0.00663934971838198,
0.00469321556579621, -0.00901979006656426, 0.035818561187916,
0.0317729134664619, 0.0243178443420379, 0.000673143881208398,
0.0749327188940092), .Dim = c(14L, 14L), .Dimnames = list(c("cc.c.protect.i",
"cc.c.privacy.i", "cc.c.limchoi.c", "cc.c.interests.i", "cc.c.goals.c",
"cc.c.harm.c", "cc.c.needs.c", "cc.h.discrim.e", "cc.h.wealth.e",
"cc.h.revdis2.h", "cc.h.equal.h", "cc.h.feminine.h", "cc.h.radeq.e",
"cc.h.tradfam.h"), c("cc.c.protect.i", "cc.c.privacy.i", "cc.c.limchoi.c",
"cc.c.interests.i", "cc.c.goals.c", "cc.c.harm.c", "cc.c.needs.c",
"cc.h.discrim.e", "cc.h.wealth.e", "cc.h.revdis2.h", "cc.h.equal.h",
"cc.h.feminine.h", "cc.h.radeq.e", "cc.h.tradfam.h")))
#Specify Model
cfa.mod1<-specifyModel()
HE -> cc.h.discrim.e, he0
HE -> cc.h.wealth.e, he1
HE -> cc.h.revdis2.h, he2
HE -> cc.h.equal.h, he3
HE -> cc.h.radeq.e, he4
HE -> cc.h.tradfam.h, he5
HE -> cc.h.feminine.h, he6
IC -> cc.c.protect.i, ic0
IC -> cc.c.privacy.i, ic1
IC -> cc.c.limchoi.c, ic2
IC -> cc.c.interests.i, ic3
IC -> cc.c.goals.c, ic4
IC -> cc.c.harm.c, ic5
IC -> cc.c.needs.c, ic6
HE <-> HE, NA, 1
IC <-> IC, NA, 1
cc.h.discrim.e <-> cc.h.discrim.e, error1
cc.h.wealth.e <-> cc.h.wealth.e, error2
cc.h.revdis2.h <-> cc.h.revdis2.h, error3
cc.h.equal.h <-> cc.h.equal.h, error4
cc.h.radeq.e <-> cc.h.radeq.e, error5
cc.h.tradfam.h <-> cc.h.tradfam.h, error6
cc.h.feminine.h <-> cc.h.feminine.h, error7
cc.c.protect.i <-> cc.c.protect.i, error8
cc.c.privacy.i <-> cc.c.privacy.i, error9
cc.c.limchoi.c <-> cc.c.limchoi.c, error10
cc.c.interests.i<-> cc.c.interests.i, error11
cc.c.goals.c <-> cc.c.goals.c, error12
cc.c.harm.c <-> cc.c.harm.c, error13
cc.c.needs.c <-> cc.c.needs.c, error14
#Test Model
cfa1<-sem(cfa.mod1, S=ff.cov, N=376)
#Examine Model
cfa1
summary(cfa1)
stdCoef(cfa1)
#First few lies of my output
Model Chisquare = 414.2874 Df = 77 Pr(>Chisq) = 1.142376e-47
AIC = 470.2874
BIC = -42.29101
*********************************
Simon J. Kiss, PhD
Assistant Professor, Wilfrid Laurier University
73 George Street
Brantford, Ontario, Canada
N3T 2C9
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