lavaan Yves Rosseel Department of Data Analysis Ghent University (Belgium) lavaan lavaan cfa sem growth summary coef fitted inspe
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1 lavaan Yves Rosseel Department of Data Analysis Ghent University (Belgium) lavaan lavaan cfa sem growth summary coef fitted inspect 2 lavaan * lavaan : CFA arakit@kansai-u.ac.jp *1 The lavaan tutorial 1
2 lavaan ˆ 1 R R ˆ lavaan lavaan / cfa sem ˆ ˆ R lavaan R R SPSS R R ˆ lavaan lavaan ˆ lavaan 2
3 ˆ lavaan groups.google.com/d/forum/lavaan/ github R 2 lavaan lavaan CRAN lavaan R install.packages("lavaan", dependencies = TRUE) > library(lavaan) This is lavaan lavaan is BETA software! Please report any bugs. 3 lavaan lavaan R y ~ x1 + x2 + x3 + x4 ~ y + lavaan f 3
4 y ~ f1 + f2 + x1 + x2 f1 ~ f2 + f3 f2 ~ f3 + x1 + x2 = ~ manifest 3 f1 f2 f3 f1 ~ y1 + y2 + y3 f2 ~ y4 + y5 + y6 f3 ~ y7 + y8 + y9 + y10 2 ~~ y1 ~~ y1 y1 ~~ y2 f1 ~~ f2 # # # 1 y1 ~ 1 f1 ~ 1 4 =~ ~ ( ) ~~ ~ 1 lavaan mymodel <- # y1 + y2 ~ f1 + f2 + x1 + x2 4
5 f1 ~ f2 + f3 f2 ~ f3 + x1 + x2 # f1 =~ y1 + y2 + y3 f2 =~ y4 + y5 + y6 f3 =~ y7 + y8 + y9 + y10 # y1 ~~ y1 y1 ~~ y2 f1 ~~ f2 # y1 ~ 1 f1 ~ 1 R R & RStudio R RStudio R mymodel # mymodel.lav Word R mymodel <- readlines("/mydirectory/mymodel.lav") readlines mymodel 4 1: CFA cfa() CFA CFA lavaan HolzingerSwineford1939 R >?HolzingerSwineford1939 5
6 SEM SEM 2 Pasteur Grant-White CFA 3 ˆ 3 x1, x2 x3 visual ˆ 3 x4, x5 x6 textual ˆ 3 x7 x8 x9 speed 3 lavaan visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 3 = ~ = ~ = ~ cfa()
7 HS.model <- visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 CFA fit <- cfa(hs.model, data = HolzingerSwineford1939) lavaan cfa() 2 summary() summary(fit, fit.measures = TRUE) SEM lavaan (0.5-13) converged normally after 41 iterations Number of observations 301 Estimator ML Minimum Function Test Statistic Degrees of freedom 24 P-value (Chi-square) Model test baseline model: Minimum Function Test Statistic Degrees of freedom 36 P-value Full model versus baseline model: Comparative Fit Index (CFI) Tucker-Lewis Index (TLI) Loglikelihood and Information Criteria: Loglikelihood user model (H0) Loglikelihood unrestricted model (H1) Number of free parameters 21 7
8 Akaike (AIC) Bayesian (BIC) Sample-size adjusted Bayesian (BIC) Root Mean Square Error of Approximation: RMSEA Percent Confidence Interval P-value RMSEA <= Standardized Root Mean Square Residual: SRMR Parameter estimates: Information Standard Errors Expected Standard Estimate Std.err Z-value P(> z ) Latent variables: visual =~ x x x textual =~ x x x speed =~ x x x Covariances: visual ~~ textual speed textual ~~ speed Variances: x x x x x x x x x visual
9 textual speed ˆ lavaan ˆ lavaan ˆ ˆ ML ˆ P fit.measures = TRUE Model test baseline model SRMR Latent Variables Covariances Variances Estimate 2 Std.err 3 Z-value Wald P(> z ) 0 p 1 3 # lavaan 1 library(lavaan) # HS.model <- visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 # fit <- cfa(hs.model, data=holzingerswineford1939) # summary(fit, fit.measures=true) R & lavaan 1. lavaan cfa() lavaan sem() growth() 3 9
10 lavaan() 3. RMSEA R PoliticalDemocracy Bollen 1989 lavaan model <- # ind60 =~ x1 + x2 + x3 dem60 =~ y1 + y2 + y3 + y4 dem65 =~ y5 + y6 + y7 + y8 # dem60 ~ ind60 dem65 ~ ind60 + dem60 # y1 ~~ y5 y2 ~~ y4 + y6 y3 ~~ y7 y4 ~~ y8 y6 ~~ y8 3 =~ ~ ~~ R ~~ lavaan y1 ~~ y y2 ~~ y4 y2 ~~ y6 y2 ~~ y4 + y6 10
11 model <- # ind60 =~ x1 + x2 + x3 dem60 =~ y1 + y2 + y3 + y4 dem65 =~ y5 + y6 + y7 + y8 # dem60 ~ ind60 dem65 ~ ind60 + dem60 # y1 ~~ y5 y2 ~~ y4 + y6 y3 ~~ y7 y4 ~~ y8 y6 ~~ y8 fit <- sem(model, data = PoliticalDemocracy) summary(fit, standardized = TRUE) lavaan (0.5-13) converged normally after 68 iterations Number of observations 75 Estimator ML Minimum Function Test Statistic Degrees of freedom 35 P-value (Chi-square) Parameter estimates: Information Standard Errors Expected Standard Estimate Std.err Z-value P(> z ) Std.lv Std.all Latent variables: ind60 =~ x x x dem60 =~ y y y y dem65 =~ y
12 y y y Regressions: dem60 ~ ind dem65 ~ ind dem Covariances: y1 ~~ y y2 ~~ y y y3 ~~ y y4 ~~ y y6 ~~ y Variances: x x x y y y y y y y y ind dem dem sem() cfa() 2 summary() fit.measures=true 2 standardized=true 2 1 Std.lv 2 Std.all 12
13 library(lavaan) # 1 model <- # measurement model ind60 =~ x1 + x2 + x3 dem60 =~ y1 + y2 + y3 + y4 dem65 =~ y5 + y6 + y7 + y8 # regressions dem60 ~ ind60 dem65 ~ ind60 + dem60 # residual correlations y1 ~~ y5 y2 ~~ y4 + y6 y3 ~~ y7 y4 ~~ y8 y6 ~~ y8 fit <- sem(model, data=politicaldemocracy) summary(fit, standardized=true) lavaan f =~ y1 + 1*y2 + 1*y3 + 1*y4 lavaan pre-multiplication Holzinger and Swineford 3 CFA CFA 0 0 visual textual 0 speed 1 1 x7 1 NA # three-factor model visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ NA*x7 + x8 + x9 # orthogonal factors visual ~~ 0*speed textual ~~ 0*speed # fix variance of speed factor speed ~~ 1*speed 13
14 CFA cfa() orthogonal=true HS.model <- visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 fit.hs.ortho <- cfa(hs.model, data = HolzingerSwineford1939, orthogonal = TRUE) CFA 1 cfa std.lv=true HS.model <- visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 fit <- cfa(hs.model, data = HolzingerSwineford1939, std.lv = TRUE) std.lv=true 1 1 lavaan start() visual =~ x1 + start(0.8)*x2 + start(1.2)*x3 textual =~ x4 + start(0.5)*x5 + start(1.0)*x6 speed =~ x7 + start(0.7)*x8 + start(1.8)*x9 1 x1 x4 x7 lavaan PolitcalDemocracy model <- # ind60 =~ x1 + x2 + x3 dem60 =~ y1 + y2 + y3 + y4 14
15 dem65 =~ y5 + y6 + y7 + y8 # dem60 ~ ind60 dem65 ~ ind60 + dem60 # y1 ~~ y5 y2 ~~ y4 + y6 y3 ~~ y7 y4 ~~ y8 y6 ~~ y8 fit <- sem(model, data=politicaldemocracy) coef(fit) ind60=~x2 ind60=~x3 dem60=~y2 dem60=~y3 dem60=~y dem65=~y6 dem65=~y7 dem65=~y8 dem60~ind60 dem65~ind dem65~dem60 y1~~y5 y2~~y4 y2~~y6 y3~~y y4~~y8 y6~~y8 x1~~x1 x2~~x2 x3~~x y1~~y1 y2~~y2 y3~~y3 y4~~y4 y5~~y y6~~y6 y7~~y7 y8~~y8 ind60~~ind60 dem60~~dem dem65~~dem coef() 3 3 mylabel x3 model <- # ind60 =~ x1 + x2 + mylabel*x3 dem60 =~ y1 + y2 + y3 + y4 dem65 =~ y5 + y6 + y7 + y8 # dem60 ~ ind60 dem65 ~ ind60 + dem60 15
16 # y1 ~~ y5 y2 ~~ y4 + y6 y3 ~~ y7 y4 ~~ y8 y6 ~~ y8 a-za-z 13bis lavaan label() ~ = * 1 f =~ y1 + y2 + mylabel*y3 + start(0.5)*y3 + y4 y3 2 y3 1 3 H&S CFA x2 x3 2 lavaan visual =~ x1 + v2*x2 + v2*x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 equal() visual =~ x1 + x2 + equal("visual=~x2")*x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 x2 visual=~x2 x3 equal() x2 16
17 0.4-8 y ~ b1*x1 + b2*x2 + b3*x3 b1 b2 b3 4 set.seed(1234) Data <- data.frame(y = rnorm(100), x1 = rnorm(100), x2 = rnorm(100), x3 = rnorm(100)) model <- y ~ b1*x1 + b2*x2 + b3*x3 fit <- sem(model, data=data) coef(fit) b1 b2 b3 y~~y b1 = (b2 + b3) 2 b1 > exp(b2 + b3) 2. 2 model.constr <- # y ~ b1*x1 + b2*x2 + b3*x3 # b1 == (b2 + b3)^2 b1 > exp(b2 + b3) model.constr <- # y ~ b1*x1 + b2*x2 + b3*x3 # b1 == (b2 + b3)^2 b1 > exp(b2 + b3) fit <- sem(model.constr, data=data) coef(fit) b1 b2 b3 y~~y b1 exp(b2 + b3) 17
18 7 1 lavaan 1 (1) 1 H&S 3 CFA # 3 visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 # x1 ~ 1 x2 ~ 1 x3 ~ 1 x4 ~ 1 x5 ~ 1 x6 ~ 1 x7 ~ 1 x8 ~ 1 x9 ~ 1 meanstructure=true H&S 3 CFA > fit <- cfa(hs.model, data = HolzingerSwineford1939, meanstructure = TRUE) > summary(fit) lavaan (0.5-13) converged normally after 41 iterations Number of observations 301 Estimator ML Minimum Function Test Statistic Degrees of freedom 24 P-value (Chi-square) Parameter estimates: Information Standard Errors Expected Standard 18
19 Estimate Std.err Z-value P(> z ) Latent variables: visual =~ x x x textual =~ x x x speed =~ x x x Covariances: visual ~~ textual speed textual ~~ speed Intercepts: x x x x x x x x x visual textual speed Variances: x x x x x x x x x visual textual speed
20 Intercept cfa() sem() x1 x2 x3 x4 0.5 # 3 visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 # x1 + x2 + x3 + x4 ~ 0.5*1 x1 ~ 0.5*1 x2 ~ 0.5*1 8 lavaan group 2 Pasteur Grant-White H&S CFA HS.model <- visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 fit <- cfa(hs.model, data=holzingerswineford1939, group="school") summary(fit) lavaan (0.5-13) converged normally after 63 iterations Number of observations per group Pasteur 156 Grant-White 145 Estimator ML Minimum Function Test Statistic Degrees of freedom 48 P-value (Chi-square) Chi-square for each group: 20
21 Pasteur Grant-White Parameter estimates: Information Standard Errors Expected Standard Group 1 [Pasteur]: Estimate Std.err Z-value P(> z ) Latent variables: visual =~ x x x textual =~ x x x speed =~ x x x Covariances: visual ~~ textual speed textual ~~ speed Intercepts: x x x x x x x x x visual textual speed Variances: x x x x x
22 x x x x visual textual speed Group 2 [Grant-White]: Estimate Std.err Z-value P(> z ) Latent variables: visual =~ x x x textual =~ x x x speed =~ x x x Covariances: visual ~~ textual speed textual ~~ speed Intercepts: x x x x x x x x x visual textual speed Variances: x x x
23 x x x x x x visual textual speed HS.model <- visual =~ x *x2 + c(0.6, 0.8)*x3 textual =~ x4 + start(c(1.2, 0.6))*x5 + a*x6 speed =~ x7 + x8 + x9 visual 1 x x2 0.5 textual x5 2 x6 a 1 2 c(a1,a2)*x6 c(a,a)*x6 1 fit <- cfa(hs.model, data = HolzingerSwineford1939, group = "school") summary(fit) lavaan (0.5-13) converged normally after 58 iterations Number of observations per group Pasteur 156 Grant-White 145 Estimator ML Minimum Function Chi-square Degrees of freedom 52 P-value (Chi-square) Chi-square for each group: Pasteur Grant-White
24 Parameter estimates: Information Standard Errors Expected Standard Group 1 [Pasteur]: Estimate Std.err Z-value P(> z ) Latent variables: visual =~ x x x textual =~ x x x speed =~ x x x Covariances: visual ~~ textual speed textual ~~ speed Intercepts: x x x x x x x x x visual textual speed Variances: x x x x x x x x
25 x visual textual speed Group 2 [Grant-White]: Estimate Std.err Z-value P(> z ) Latent variables: visual =~ x x x textual =~ x x x speed =~ x x x Covariances: visual ~~ textual speed textual ~~ speed Intercepts: x x x x x x x x x visual textual speed Variances: x x x x x x
26 x x x visual textual speed x3 HS.model <- visual =~ x1 + x2 + c(v3,v3)*x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 group.equal HS.model <- visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 fit <- cfa(hs.model, data=holzingerswineford1939, group="school", group.equal=c("loadings")) summary(fit) lavaan (0.5-13) converged normally after 46 iterations Number of observations per group Pasteur 156 Grant-White 145 Estimator ML Minimum Function Test Statistic Degrees of freedom 54 P-value (Chi-square) Chi-square for each group: Pasteur Grant-White
27 Parameter estimates: Information Standard Errors Expected Standard Group 1 [Pasteur]: Estimate Std.err Z-value P(> z ) Latent variables: visual =~ x x x textual =~ x x x speed =~ x x x Covariances: visual ~~ textual speed textual ~~ speed Intercepts: x x x x x x x x x visual textual speed Variances: x x x x x x x x
28 x visual textual speed Group 2 [Grant-White]: Estimate Std.err Z-value P(> z ) Latent variables: visual =~ x x x textual =~ x x x speed =~ x x x Covariances: visual ~~ textual speed textual ~~ speed Intercepts: x x x x x x x x x visual textual speed Variances: x x x x x x
29 x x x visual textual speed ˆ intercepts ˆ means / ˆ residuals ˆ residual.covariances ˆ lv.variances ˆ lv.covariances ˆ regressions group.equal group.partial fit <- cfa(hs.model, data=holzingerswineford1939, group="school", group.equal=c("loadings", "intercepts"), group.partial=c("visual=~x2", "x7~1")) CFA measurementinvariance() 0.5 measurementinvariance() semtools 2 cfi lavaan measurementinvariance() library(semtools) measurementinvariance(hs.model, data=holzingerswineford1939, group="school") Measurement invariance tests: Model 1: configural invariance: 29
30 chisq df pvalue cfi rmsea bic Model 2: weak invariance (equal loadings): chisq df pvalue cfi rmsea bic [Model 1 versus model 2] delta.chisq delta.df delta.p.value delta.cfi Model 3: strong invariance (equal loadings + intercepts): chisq df pvalue cfi rmsea bic [Model 1 versus model 3] delta.chisq delta.df delta.p.value delta.cfi [Model 2 versus model 3] delta.chisq delta.df delta.p.value delta.cfi Model 4: equal loadings + intercepts + means: chisq df pvalue cfi rmsea bic [Model 1 versus model 4] delta.chisq delta.df delta.p.value delta.cfi [Model 3 versus model 4] delta.chisq delta.df delta.p.value delta.cfi group.partial Demo.growth # 4 30
31 # i =~ 1*t1 + 1*t2 + 1*t3 + 1*t4 s =~ 0*t1 + 1*t2 + 2*t3 + 3*t4 lavaan growth() model <- i =~ 1*t1 + 1*t2 + 1*t3 + 1*t4 s =~ 0*t1 + 1*t2 + 2*t3 + 3*t4 fit <- growth(model, data=demo.growth) summary(fit) lavaan (0.5-13) converged normally after 44 iterations Number of observations 400 Estimator ML Minimum Function Test Statistic Degrees of freedom 5 P-value (Chi-square) Parameter estimates: Information Standard Errors Expected Standard Estimate Std.err Z-value P(> z ) Latent variables: i =~ t t t t s =~ t t t t Covariances: i ~~ s Intercepts: t t t t i s
32 Variances: t t t t i s growth() sem() 0 / 2 x1 x2 4 lavaan # # i =~ 1*t1 + 1*t2 + 1*t3 + 1*t4 s =~ 0*t1 + 1*t2 + 2*t3 + 3*t4 # i ~ x1 + x2 s ~ x1 + x2 # t1 ~ c1 t2 ~ c2 t3 ~ c3 t4 ~ c4 32
33 & R # model <- # i =~ 1*t1 + 1*t2 + 1*t3 + 1*t4 s =~ 0*t1 + 1*t2 + 2*t3 + 3*t4 # i ~ x1 + x2 s ~ x1 + x2 # t1 ~ c1 t2 ~ c2 t3 ~ c3 t4 ~ c4 fit <- growth(model, data=demo.growth) summary(fit) /1 1, 2, 3,... K K > 2 K 1 lavaan WLS R ordered() Data 4 item1, item2, item3, item4) Data[,c("item1", "item2", "item3", 33
34 "item4")] <- lapply(data[,c("item1", "item2", "item3", "item4")], ordered) 2. cfa sem growth lavaan 1 ordered= 4 2 item1, item2, item3, item4 > fit <- cfa(mymodel, data=mydata, ordered=c("item1","item2", "item3","item4")) lavaan WLSMV 2 DWLS 11 lower < wheaton.cov <- getcov(lower, names=c("anomia67", "powerless67", "anomia71", "powerless71", "education","sei")) getcov() 2 getcov() 34
35 # Wheaton et al wheaton.model <- # ses =~ education + sei alien67 =~ anomia67 + powerless67 alien71 =~ anomia71 + powerless71 # alien71 ~ alien67 + ses alien67 ~ ses # anomia67 ~~ anomia71 powerless67 ~~ powerless71 fit <- sem(wheaton.model, sample.cov=wheaton.cov, sample.nobs=932) summary(fit, standardized=true) lavaan (0.5-13) converged normally after 82 iterations Number of observations 932 Estimator ML Minimum Function Test Statisti Degrees of freedom 4 P-value (Chi-square) Parameter estimates: Information Standard Errors Expected Standard Estimate Std.err Z-value P(> z ) Std.lv Std.all Latent variables: ses =~ education sei alien67 =~ anomia powerless alien71 =~ anomia powerless Regressions: alien71 ~ alien
36 ses alien67 ~ ses Covariances: anomia67 ~~ anomia powerless67 ~~ powerless Variances: education sei anomia powerless anomia powerless ses alien alien sample.cov sample.mean sample.nobs 12 lavaan estimator = "ML" lavaan ˆ "GLS" 2 ˆ "WLS" 2 ADF ˆ "DWLS" 2 ˆ "ULS" 2 lavaan ˆ "MLM" Satorra-Bentler ˆ "MLMVS" Satterthwaite ˆ "MLMV" (scaleshifted ). ˆ "MLF" 1 36
37 ˆ "MLR" Huber-White Yuan-Bentler lavaan DWLS ULS WLSM, WLSMVS, WLSMV, ULSM, ULSMVS ULSMV WLS Wishert "ML" lavaan n 1 n 2 n n 1 Mplus 2 n 1 likelihood="wishart" fit <- cfa(hs.model, data = HolzingerSwineford1939, likelihood = "wishart") fit lavaan (0.5-13) converged normally after 41 iterations Number of observations 301 Estimator ML Minimum Function Chi-square Degrees of freedom 24 P-value (Chi-square) EQ LISREL AMOS Wishart Mplus MCAR MAR lavaan missing="ml" h1 ML missing="ml" information "expected" "observed" "ML" se "robust.sem" "robust.huber.white" "first.order" "boootstrap" 37
38 "none" "test" "standard" "Satorra-Bentler" "Yuan-Bentler" "bootstrap" lavaan 2 se="bootstrap" test="bootstrap" p bootstraplavaan() lavaan 13 Y X M 3 3 X Y X M Y set.seed(1234) X <- rnorm(100) M <- 0.5*X + rnorm(100) Y <- 0.7*M + rnorm(100) Data <- data.frame(x = X, Y = Y, M = M) model <- # Y ~ c*x # M ~ a*x Y ~ b*m # (a*b) ab := a*b # total := c + (a*b) fit <- sem(model, data=data) summary(fit) lavaan (0.5-13) converged normally after 13 iterations Number of observations 100 Estimator ML Minimum Function Test Statistic Degrees of freedom 0 P-value (Chi-square) Parameter estimates: Information Standard Errors Expected Standard 38
39 Estimate Std.err Z-value P(> z ) Regressions: Y ~ X (c) M ~ X (a) Y ~ M (b) Variances: Y M Defined parameters: ab total lavaan := se="bootstrap" 14 summary() modindices=true modindices() modindices() fit <- cfa(hs.model, data=holzingerswineford1939) mi <- modindices(fit) mi[mi$op == "=~",] #$ lhs op rhs mi epc sepc.lv sepc.all sepc.nox 1 visual =~ x1 NA NA NA NA NA 2 visual =~ x visual =~ x visual =~ x visual =~ x visual =~ x visual =~ x visual =~ x visual =~ x textual =~ x textual =~ x
40 12 textual =~ x textual =~ x4 NA NA NA NA NA 14 textual =~ x textual =~ x textual =~ x textual =~ x textual =~ x speed =~ x speed =~ x speed =~ x speed =~ x speed =~ x speed =~ x speed =~ x7 NA NA NA NA NA 26 speed =~ x speed =~ x EPC epc 3 EPC sepc.lv sepc.all sepc.nox 15 summary() coef() parameterestimates parameterestimates() z fit <- cfa(hs.model, data = HolzingerSwineford1939) parameterestimates(fit) lhs op rhs est se z pvalue ci.lower ci.upper 1 visual =~ x NA NA visual =~ x visual =~ x textual =~ x NA NA textual =~ x textual =~ x speed =~ x NA NA speed =~ x speed =~ x x1 ~~ x x2 ~~ x x3 ~~ x x4 ~~ x
41 14 x5 ~~ x x6 ~~ x x7 ~~ x x8 ~~ x x9 ~~ x visual ~~ visual textual ~~ textual speed ~~ speed visual ~~ textual visual ~~ speed textual ~~ speed standardizedsolution standardizedsolution() parameterestimates() fitted.values fitted() fitted.values() fit <- cfa(hs.model, data = HolzingerSwineford1939) fitted(fit) $cov x1 x2 x3 x4 x5 x6 x7 x8 x9 x x x x x x x x x $mean x1 x2 x3 x4 x5 x6 x7 x8 x resid() residuals() normalized standardized NA fit <- cfa(hs.model, data=holzingerswineford1939) resid(fit, type="standardized") $cov 41
42 x1 x2 x3 x4 x5 x6 x7 x8 x9 x1 NA x NA x x NA x NA x NA NA x x NA x NA NA $mean x1 x2 x3 x4 x5 x6 x7 x8 x vcov vcov() AIC BIC AIC BIC AIC BIC fitmeasures fitmeasures() lavaan 1 CFI 2 fit <- cfa(hs.model, data = HolzingerSwineford1939) fitmeasures(fit) fmin chisq df pvalue baseline.chisq baseline.df baseline.pvalue cfi tli nnfi rfi nfi pnfi ifi rni logl unrestricted.logl npar aic bic ntotal bic2 rmsea rmsea.ci.lower rmsea.ci.upper rmsea.pvalue rmr rmr_nomean srmr srmr_nomean cn_05 cn_ gfi agfi pgfi mfi ecvi CFI 2 42
43 fit <- cfa(hs.model, data = HolzingerSwineford1939) fitmeasures(fit, "cfi") cfi fit <- cfa(hs.model, data = HolzingerSwineford1939) fitmeasures(fit, c("cfi", "rmsea", "srmr") cfi rmsea srmr inspect lavaan cfa() sem() growth() inspect() lavaan inspect() fit <- cfa(hs.model, data = HolzingerSwineford1939) inspect(fit) $lambda visual textul speed x x x x x x x x x $theta x1 x2 x3 x4 x5 x6 x7 x8 x9 x1 7 x2 0 8 x x x x x
44 x x $psi visual textul speed visual 16 textual speed inspect(fit, what="start") $lambda visual textul speed x x x x x x x x x $theta x1 x2 x3 x4 x5 x6 x7 x8 x9 x x x x x x x x x $psi visual textul speed visual 0.05 textual speed lavaan inspect(fit, what="list") id lhs op rhs user group free ustart exo label eq.id unco 44
45 1 1 visual =~ x visual =~ x NA visual =~ x NA textual =~ x textual =~ x NA textual =~ x NA speed =~ x speed =~ x NA speed =~ x NA x1 ~~ x NA x2 ~~ x NA x3 ~~ x NA x4 ~~ x NA x5 ~~ x NA x6 ~~ x NA x7 ~~ x NA x8 ~~ x NA x9 ~~ x NA visual ~~ visual NA textual ~~ textual NA speed ~~ speed NA visual ~~ textual NA visual ~~ speed NA textual ~~ speed NA partable(fit) inspect lavaan class?lavaan 45
lavaan: R 0.5-12 Yves Rosseel Department of Data Analysis Ghent University (Belgium) 2012 12 19 2013 1 24 lavaan lavaan * 1 1 2 2 lavaan 3 3 3 3.1......................... 4 3.2.........................
1 Stata SEM LightStone 4 SEM 4.. Alan C. Acock, Discovering Structural Equation Modeling Using Stata, Revised Edition, Stata Press 3.
1 Stata SEM LightStone 4 SEM 4.. Alan C. Acock, 2013. Discovering Structural Equation Modeling Using Stata, Revised Edition, Stata Press 3. 2 4, 2. 1 2 2 Depress Conservative. 3., 3,. SES66 Alien67 Alien71,
1 Stata SEM LightStone 3 2 SEM. 2., 2,. Alan C. Acock, Discovering Structural Equation Modeling Using Stata, Revised Edition, Stata Press.
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1 Stata SEM LightStone 1 5 SEM Stata Alan C. Acock, Discovering Structural Equation Modeling Using Stata, Revised Edition, Stata Press. Introduc
1 Stata SEM LightStone 1 5 SEM Stata Alan C. Acock, 2013. Discovering Structural Equation Modeling Using Stata, Revised Edition, Stata Press. Introduction to confirmatory factor analysis 9 Stata14 2 1
yamadaiR(cEFA).pdf
R 2012/10/05 Kosugi,E.Koji (Yamadai.R) Categorical Factor Analysis by using R 2012/10/05 1 / 9 Why we use... 3 5 Kosugi,E.Koji (Yamadai.R) Categorical Factor Analysis by using R 2012/10/05 2 / 9 FA vs
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Q10-2 テキスト P191 1. 記述統計量 ( 変数 :YY95) 表示変数として 平均 中央値 最大値 最小値 標準偏差 観測値 を選択 A. 都道府県別 Descriptive Statistics for YY95 Categorized by values of PREFNUM Date: 05/11/06 Time: 14:36 Sample: 1990 2002 Included
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講義のーと : データ解析のための統計モデリング. 第５回
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Title 講義のーと : データ解析のための統計モデリング Author(s) 久保, 拓弥 Issue Date 2008 Doc URL http://hdl.handle.net/2115/49477 Type learningobject Note この講義資料は, 著者のホームページ http://hosho.ees.hokudai.ac.jp/~kub ードできます Note(URL)http://hosho.ees.hokudai.ac.jp/~kubo/ce/EesLecture20
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kubostat2017c p (c) Poisson regression, a generalized linear model (GLM) : :
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流通科学大学論集 経済 情報 政策編 第 22 巻第 号,83-98(203) 企業分析と因果分析 Business Analysis and Causal Analysis 野口博司 * ** 磯貝恭史 Hiroshi Noguchi, Takafumi Isogai 次元縮約を行い探索的に要因構造を探る方法論については 前回に報告した 一方 最初から要因構造を想定し それを検証する方法論としては
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表示がやや変である (+2E などが買ってに加わっている 3 つの矢印をクリックす変数の正確な値が表示される その正確な値を使って次の式を書くことができる Y = 1571.73+ 258.50 pop 1913. 85 trashbag 以下の SPSS AMOS で算出した価と一致していことを確認してほしい 23 View > Standardized Estimates を選択する すると以下のような標準化係数が得られる
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第 4 章 この章では 最小二乗法をベースにして 推計上のさまざまなテクニックを検討する 変数のバリエーション 係数の制約係数にあらかじめ制約がある場合がある たとえばマクロの生産関数は 次のように表すことができる 生産要素は資本と労働である 稼動資本は資本ストックに稼働率をかけることで計算でき 労働投入量は 就業者数に総労働時間をかけることで計算できる 制約を掛けずに 推計すると次の結果が得られる
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