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1、Latent Variable Modeling Using Mplus: Day 1 Bengt Muth en FORMAT = 1f8.2 47f7.2; VARIABLE:NAMES = id weight0 weight8 weight18 weigh36 height0 height8 height18 height36 hcirc0 hcirc8 hcirc18 hcirc36 mo- malc1 momalc2 momalc3 momalc8 momalc18 momalc36 momcig1 momcig2 momcig3 momcig8 momcig18 momcig36
2、gender eth momht gestage age8 age18 age36 esteem8 es- teem18 esteem36 faminc0 faminc8 faminc18 faminc36 mom- drg36 gravid sick8 sick18 sick36 advp advm1 advm2 advm3; MISSING = ALL (999); USEVARIABLES = momalc3 momcig3 hcirc0 hcirc36 gender eth; USEOBSERVATIONS = id NE 1121 AND NOT (momalc1 EQ 999 AN
3、D momalc2 EQ 999 AND momalc3 EQ 999); Bengt Muth en hcirc36 = hcirc36/10; momalc3 = log(momalc3 +1); MODEL:hcirc36 ON hcirc0 gender eth; hcirc0 ON momalc3 momcig3 gender eth; MODEL INDIRECT:hcirc36 IND hcirc0 momalc3; hcirc36 IND hcirc0 momcig3; OUTPUT:SAMPSTAT STANDARDIZED; Bengt Muth en USEOBSERVA
4、TIONS = school EQ 0; ANALYSIS:TYPE = EFA 1 6; ROTATION = GEOMIN; ! default ESTIMATOR = ML; ! default PARALLEL = 50; OUTPUT:SAMPSTAT MODINDICES; PLOT:TYPE = PLOT3; Bengt Muth en Holzinger-Swineford (1939) 24-variable model Testlet modeling, e.g. for PISA test items Longitudinal modeling with across-t
5、ime correlation for residuals Bi-factor modeling is as popular today as in 1939. New developments for faster maximum-likelihood estimation with categorical items, reducing the number of dimensions for numerical integration: Gibbons, USEOBSERVATIONS = school EQ 0; ANALYSIS:TYPE = EFA 5 5; ROTATION =
6、BI-GEOMIN; Bengt Muth en it is just another rotation of the factors For the 24-variable Holzinger-Swineford data, bi-factor EFA with 1 general and 4 specifi c factors gives a simple factor pattern that largely agrees with the Holzinger-Swineford hypotheses In contrast, regular 5-factor EFA for the 2
7、4-variable Holzinger-Swineford data does not give a simple factor loading pattern Bengt Muth en Gelman et al., 1996, Scheines et al., 1999) can be obtained via a fi t statistic based on the usual chi-square test of H0against H1. Low PPP indicates poor fi t A 95% confi dence interval is produced for
8、the difference in chi-square for the real and replicated data; negative lower limit is good Sensitivity analysis is recommended for the choice of variance for the informative priors: How much do key parameters change as the prior variance is changed? As the variances of the informative priors are ma
9、de larger, PPP increases and reaches a peak. SEs of estimates also increase and at some point the iterations wont converge (model is not identifi ed) Bengt Muth en USEV = visual-fi gurew; USEOBS = school eq 0; DEFINE: STANDARDIZE visual-fi gurew; ANALYSIS:ESTIMATOR = BAYES; PROCESSORS = 2; FBITER =
10、10000; Bengt Muth en verbal BY general* paragrap sentence wordc wordm; speed BY addition* code counting straight; memory BY wordr* numberr fi gurer object numberf fi gurew; spatial-memory1; ! cross-loadings: spatial BY general-fi gurew*0 (a1-a15); verbal BY visual-fl ags*0 (b1-b4); verbal BY additio
11、n-fi gurew*0 (b5-b14); speed BY visual-wordm*0 (c1-c9); speed BY wordr-fi gurew*0 (c10-c15); memory BY visual-straight*0 (d1-d13); MODEL PRIORS: a1-d13 N(0,0.01); OUTPUT:TECH1 TECH8 STDY; PLOT:TYPE = PLOT2; Bengt Muth en acceptable degree of shrinkage monitored by PPP Bayes modifi cation indices obt
12、ained by estimated cross-loadings Factor correlations: EFA 01log hd 00999 999999999 Bengt Muth en FORMAT = 2f5, f2, t14, 5f7, t50, f8, t60, 6f1.0, t67, 2f2.0, t71, 8f1.0, t79, f2.0, t82, 4f2.0; DATA TWOPART: NAMES = hd82-hd89; BINARY = u18 u19 u20 u24 u25; CONTINUOUS = y18 y19 y20 y24 y25; Bengt Mut
13、h en USEOBSERVATIONS = cohort EQ 64 AND (coll GT 0 AND coll LT 20); USEVARIABLES = male black hisp es fh123 hsdrp coll u18- u25 y18-y25; CATEGORICAL = u18-u25; MISSING = .; AUXILIARY = hd82-hd89; DEFINE:CUT coll (12.1); ANALYSIS:ESTIMATOR = ML; ALGORITHM = INTEGRATION; COVERAGE = 0.09; Bengt Muth en
14、 iy sy qy | y18-3.008 y19-2.197 y20-1.621 y24-.235 y25.000; iu-qy ON male black hisp es fh123 hsdrp coll; OUTPUT:TECH1 TECH4 TECH8 STANDARDIZED; PLOT:TYPE = PLOT3; SERIES = y18-y25(sy) | u18-u25(su); Bengt Muth en CATEGORICAL = stub1f-tease7s; MISSING = ALL (999); DEFINE:CUT stub1f-tease7s (1.5); AN
15、ALYSIS:ESTIMATOR = BAYES; PROCESSORS = 2; MODEL:f1f by stub1f-tease1f* (lam11-lam19); f1s by stub1s-tease1s* (lam21-lam29); f2s by stub2s-tease2s* (lam31-lam39); f3s by stub3s-tease3s* (lam41-lam49); f4s by stub4s-tease4s* (lam51-lam59); f5s by stub5s-tease5s* (lam61-lam69); f6s by stub6s-tease6s* (
16、lam71-lam79); f7s by stub7s-tease7s* (lam81-lam89); f1f1; Bengt Muth en stub1s$1-tease1s$1 (tau21-tau29); stub2s$1-tease2s$1 (tau31-tau39); stub3s$1-tease3s$1 (tau41-tau49); stub4s$1-tease4s$1 (tau51-tau59); stub5s$1-tease5s$1 (tau61-tau69); stub6s$1-tease6s$1 (tau71-tau79); stub7s$1-tease7s$1 (tau81-tau89); f1f-f7s0; i s q | f1f0 f1s0.5 f2s1.5 f3s2.5 f4s3.5 f5s4.5 f6s5.5 f7s6.5; q0; MODEL PRIORS:DO(1,9) DIFF(lam1#-lam8#) N(0,.01); DO(1,9) DIFF
