Minor data correction
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1 More adventures
2 Steps of analysis I. Initial data entry as a spreadsheet II. descriptive stats III.preliminary correlational structure IV.EFA V.CFA/SEM VI.Theoretical interpretation
3 Initial data entry > megan <- read.clipboard() > describe(megan) var n mean sd median trimmed mad min max range skew kurtosis se adult adult adult revadult revadult revadult adult adult adult adult adult revadult adult > Clearly, a missing value code of -999 was used
4 Minor data correction > megan[megan == -999] <- NA > describe(megan) var n mean sd median trimmed mad min max range skew kurtosis se adult adult adult revadult revadult revadult adult adult adult adult adult revadult adult
5 Graphics: SPLOM adult adult3 adult2 revadult5 revadult adult8 adult adult7 revadult6 adult adult adult3 revadult2
6 Cluster structure revadult2 revadult5 revadult revadult6 adult adult2 adult3 adult9 adult7 adult8 adult adult0 adult C C C3 C ICLUST C5 C8 C6 C C C C 0.9 C2 > ic.meg <- ICLUST(megan) Loading required package: Rgraph Loading required package: graph Loading required package: grid > ic.meg ICLUST (Item Cluster Analysis) Call: ICLUST(r.mat = megan) Item by Cluster Structure matrix [,] adult 0.53 adult adult3 0.6 revadult 0.56 revadult5 0.5 revadult adult adult adult adult adult 0.8 revadult2 0. adult3 0.8 With eigenvalues of: []. Purified scale intercorrelations reliabilities on diagonal correlations corrected for attenuation above diagonal: [,] [,] 0.88
7 Theory says 2 adult adult2 adult3 adult9 adult7 adult8 adult adult0 adult3 revadult2 revadult5 revadult revadult6 clusters C C2 ICLUST C3 C C8 C6 C7 C C0 C C > ic2 ICLUST (Item Cluster Analysis) Call: ICLUST(r.mat = megan, nclusters = 2) Item by Cluster Structure matrix: C C9 adult adult adult revadult revadult revadult adult adult adult adult adult revadult adult With eigenvalues of: C C Purified scale intercorrelations reliabilities on diagonal correlations corrected for attenuation above diagonal: C C9 C C
8 Sort the loadings > ICLUST.sort(ic2) $sorted item content cluster C C9 adult8 8 adult adult3 3 adult adult7 7 adult adult2 2 adult adult0 0 adult adult9 9 adult adult adult adult3 3 adult adult adult revadult revadult revadult6 6 revadult revadult5 5 revadult revadult2 2 revadult
9 VSS suggests or 2 Very Simple Structure Very Simple Structure Fit Number of Factors
10 VSS says or 2 > vss <- VSS(megan) > vss Very Simple Structure Call: VSS(x = megan) VSS complexity achieves a maximimum of 0.79 with factors VSS complexity 2 achieves a maximimum of 0.88 with 2 factors The Velicer MAP criterion achieves a minimum of 0.7 with 2 factors Velicer MAP [] Very Simple Structure Complexity [] Very Simple Structure Complexity 2 []
11 Parallel Analysis Parallel Analysis Scree Plots eigenvalues of principal components and factor analysis PC Actual Data PC Simulated Data PC Resampled Data FA Actual Data FA Simulated Data FA Resampled Data 2 PCs 3- Factors Factor Number
12 Omega Omega adult adult2 adult3 revadult revadult5 revadult6 adult7 adult8 adult9 adult0 adult revadult2 adult3 g F* F2* F3* Omega adult adult2 adult3 revadult revadult5 revadult6 adult7 adult8 adult9 adult0 adult revadult2 adult3 g F F2 F om <- omega(megan) om.h <- omega(megan,sl=false)
13 > om Omega Call: omega(m = megan) Alpha: 0.88 G.6: 0.9 Omega Hierarchical: 0.69 Omega Total 0.9 Schmid Leiman Factor loadings greater than 0.2 g F* F2* F3* h2 u2 adult adult adult revadult revadult revadult adult adult adult adult adult revadult adult With eigenvalues of: g F* F2* F3* general/max 2.56 max/min = 3.3 > Omega fits, but badly The degrees of freedom for the model is 2 and the fit was 0.3 The number of observations was 302 with Chi Square = with prob < 5.9e-05
14 sem of bifactor > mod <- sem(om$model,cov(megan,use="pairwise"),285) > summary(mod,digits=2) Model Chisquare = 83 Df = 52 Pr(>Chisq) = Chisquare (null model) = 55 Df = 78 Goodness-of-fit index = 0.96 Adjusted goodness-of-fit index = 0.93 RMSEA index = % CI: (0.026, 0.06) Bentler-Bonnett NFI = 0.95 Tucker-Lewis NNFI = 0.97 Bentler CFI = 0.98 SRMR = BIC = -2 Normalized Residuals Min. st Qu. Median Mean 3rd Qu. Max. -.e e-0 3.9e e e-0.9e+00
15 Standardized coefficients > std.coef(mod,digits=2) Std. Estimate adult adult adult <--- g adult2 adult adult2 <--- g adult3 adult adult3 <--- g revadult revadult 0.28 revadult <--- g revadult5 revadult revadult5 <--- g revadult6 revadult revadult6 <--- g adult7 adult adult7 <--- g adult8 adult adult8 <--- g adult9 adult adult9 <--- g adult0 adult adult0 <--- g adult adult 0.5 adult <--- g revadult2 revadult revadult2 <--- g adult3 adult adult3 <--- g F3*adult F3*adult 0.07 adult <--- F3* F3*adult2 F3*adult adult2 <--- F3* F3*adult3 F3*adult adult3 <--- F3* F2*revadult F2*revadult 0.72 revadult <--- F2* F2*revadult5 F2*revadult revadult5 <--- F2* F2*revadult6 F2*revadult revadult6 <--- F2* F*adult7 F*adult7-0.0 adult7 <--- F* F*adult8 F*adult8-0.5 adult8 <--- F* F*adult9 F*adult adult9 <--- F* F*adult0 F*adult0 0.8 adult0 <--- F* F*adult F*adult 0.25 adult <--- F* F2*revadult2 F2*revadult revadult2 <--- F2* F*adult3 F*adult adult3 <--- F*
16 Hierarchical solution > mod.h <- sem(om.h$model,cov(megan,use="pairwise"),285) > summary(mod.h,digits=2) Model Chisquare = 30 Df = 62 Pr(>Chisq) = 9.2e-07 Chisquare (null model) = 55 Df = 78 Goodness-of-fit index = 0.93 Adjusted goodness-of-fit index = 0.9 RMSEA index = % CI: (0.07, 0.077) Bentler-Bonnett NFI = 0.92 Tucker-Lewis NNFI = 0.9 Bentler CFI = 0.95 SRMR = 0.06 BIC = -220 Normalized Residuals Min. st Qu. Median Mean 3rd Qu. Max
17 Standardized coefficients for hierarchical model > std.coef(mod.h,digits=2) Std. Estimate gf gf 0.89 F <--- g gf2 gf F2 <--- g gf3 gf3 0.9 F3 <--- g F3adult F3adult 0.62 adult <--- F3 F3adult2 F3adult adult2 <--- F3 F3adult3 F3adult adult3 <--- F3 F2revadult F2revadult 0.83 revadult <--- F2 F2revadult5 F2revadult revadult5 <--- F2 F2revadult6 F2revadult6 0.7 revadult6 <--- F2 Fadult7 Fadult adult7 <--- F Fadult8 Fadult adult8 <--- F Fadult9 Fadult adult9 <--- F F3adult0 F3adult adult0 <--- F3 Fadult Fadult 0.9 adult <--- F F2revadult2 F2revadult revadult2 <--- F2 Fadult3 Fadult adult3 <--- F
18 Predicting delinquency I. Wave data, children are 2-3 II. Wave 2 data, children are 8-9 III.First do simple models, then do the panel wave data
19 Delinquency > lindsay <- read.clipboard(sep="\t") > dim(lindsay) [] 29 7 > describe(lindsay) var n mean sd median trimmed mad min max range skew kurtosis se malew momwarmw momcommunicationw momrelationshipw dadwarmw dadcommunicationw dadrelationshipw timehomew peoplehangw clothingw tvtimew closemomw closedadw momcaresw dadcaresw delinquencyw delinquencyw
20 Hard to predict criterion malew delinquencyw 0.08 delinquencyw
21 Simple models ICLUST closedadw dadcaresw delinquencyw dadwarmw C C C C2 dadcommunicationw C6 dadrelationshipw malew delinquencyw3 timehomew tvtimew peoplehangw clothingw closemomw momcaresw momwarmw C C2 C C C C3 C0 0.6 C C2 C0 C C C C momcommunicationw C momrelationshipw
22 > ic.lind ICLUST (Item Cluster Analysis) Call: ICLUST(r.mat = lindsay) Item by Cluster Structure matrix: C0 C2 C malew momwarmw momcommunicationw momrelationshipw dadwarmw dadcommunicationw dadrelationshipw timehomew peoplehangw clothingw tvtimew closemomw closedadw momcaresw dadcaresw delinquencyw delinquencyw With eigenvalues of: C0 C2 C ICLUST stats Purified scale intercorrelations reliabilities on diagonal correlations corrected for attenuation above diagonal: C2 C0 C C C C >
23 Drop criterion ICLUST closedadw dadcaresw dadwarmw C C6 0.9 C0 dadcommunicationw dadrelationshipw C5 malew timehomew tvtimew C8 0.7 C 0.68 C2 peoplehangw C2 clothingw closemomw momcaresw momwarmw momcommunicationw momrelationshipw C C C C9 C0 C9 C2 C C C
24 > ic.lind <- ICLUST(lindsay[:5]) > ic.lind ICLUST (Item Cluster Analysis) Call: ICLUST(r.mat = lindsay[:5]) ICLUST stats Item by Cluster Structure matrix: C0 C9 C2 malew momwarmw momcommunicationw momrelationshipw dadwarmw dadcommunicationw dadrelationshipw timehomew peoplehangw clothingw tvtimew closemomw closedadw momcaresw dadcaresw With eigenvalues of: C0 C9 C Purified scale intercorrelations reliabilities on diagonal correlations corrected for attenuation above diagonal: C0 C9 C2 C C C
25 > lind.keys <- make.keys(7,list(mom=c(2,3,,2,),dad=c(5,6,7,3,5), rec=c(7:0),del=c(6,7))) > rownames(lind.keys) <- colnames(lindsay) > lind.keys mom dad rec del malew momwarmw momcommunicationw momrelationshipw dadwarmw dadcommunicationw dadrelationshipw 0 0 timehomew peoplehangw clothingw tvtimew closemomw closedadw momcaresw dadcaresw delinquencyw delinquencyw > lind <- score.items(lind.keys,lindsay) sum scores
26 > lind Alpha: mom dad rec del [,] Average item correlation: mom dad rec del [,] Scale intercorrelations: mom dad rec del mom dad rec del Scale intercorrelations corrected for attenuation raw correlations below the diagonal, alpha on the diagonal corrected correlations above the diagonal: mom dad rec del mom dad rec del scales Item by scale correlations: mom dad rec del malew momwarmw momcommunicationw momrelationshipw dadwarmw dadcommunicationw dadrelationshipw timehomew peoplehangw clothingw tvtimew closemomw closedadw momcaresw dadcaresw delinquencyw delinquencyw
27 > lind.keys <- make.keys(7,list(mom=c(2,3,,2,),dad=c(5,6,7,3,5), rec=c(7:0),del=c(6,7),del=c(6),del2=c(7))) > lind <- score.items(lind.keys,lindsay) > lind Alpha: mom dad rec del del del2 [,] Average item correlation: more scales mom dad rec del del del2 [,] Scale intercorrelations: mom dad rec del del del2 mom dad rec del del del Scale intercorrelations corrected for attenuation raw correlations below the diagonal, alpha on the diagonal corrected correlations above the diagonal: mom dad rec del del del2 mom dad rec del del del
28 item correlations Item by scale correlations: mom dad rec del del del2 malew momwarmw momcommunicationw momrelationshipw dadwarmw dadcommunicationw dadrelationshipw timehomew peoplehangw clothingw tvtimew closemomw closedadw momcaresw dadcaresw delinquencyw delinquencyw
29 > mat.regress(lind$cor,c(:3),c(:6)) $beta del del del2 mom dad rec $R del del del $R2 del del del Multiple R
30 > mat.regress(lind$cor,c(:3),c(:6),n.obs=29) $beta del del del2 mom dad rec $se del del del2 mom dad rec $t del del del2 mom dad rec $Probability del del del2 mom dad rec $R del del del $R2 del del del $shrunkenr2 del del del $ser2 del del del $F del del del Multiple stats $probf del del del $df [] 3 287
31 > lind.keys <- make.keys(7,list(mom=c(2,3,,2,),dad=c(5,6,7,3,5), rec=c(7:0),del=c(6,7),del=c(6),del2=c(7),male=c())) > lind <- score.items(lind.keys,lindsay) > lind Alpha: mom dad rec del del del2 male [,] Average item correlation: mom dad rec del del del2 male [,] Add gender Scale intercorrelations: mom dad rec del del del2 male mom dad rec del del del male
32 > mat.regress(lind$cor,c(:3,7),c(:6),n.obs=29) $beta del del del2 mom dad rec male $se del del del2 mom dad rec male $t del del del2 mom dad rec male $Probability del del del2 mom dad rec male $R del del del $R2 del del del $shrunkenr2 del del del $ser2 del del del $F del del del Multiple R with gender $probf del del del $df [] 286
33 sem of delinquency
34 Final comments I. Theory first II. Measurement model III.structural model IV.Theory last
35 Theory first I. What are the constructs of interest II. How do we identify them III.What are the observed variables A.how well do they measure latent constructs IV.What is the presumed causal structure
36 Measurement model I. How many latent variables II. How well are they measured III.What are alternative models A.factors versus components B. simple structure, hierarchical structure, bifactor models, circumplex, simplex
37 Structural model I. Direction of causality II. Parsimony versus fit III.Alternative structural models A.equivalent models B. nested models
38 Theory I. What have we learned that we did not know II. What do we know is wrong that we used to think was right
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