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1、Latent Variable Modeling Using Mplus: Day 3Bengt Muth en improved unrotated starting values and standard errorsBengt Muth en SAVE=FS(300); FACTORS=factornames; This command specifies that 300 imputations will be used to estimate the factor scores and that plausible value distributions are available
2、for plottingPosterior mean, median, confidence intervals, standard error, all imputed values, distribution plot for each factor score for each latent variable for any model estimated with the Bayes estimatorBayes factor score advantages: more accurate than ML factor scores in small sample size, Baye
3、s factor score more accurate in secondary analysis such as for example computing correlations between factorBengt Muth en MISSING = ALL(-999); !CLUSTER = hosp; GROUPING = hosp (101 102 104 105 201 301-306 308 310-314 316-320 322 401-403 405-409 412-416 501-503 505-512 602-609 612-613 701 801 901-908
4、); ANALYSIS:ESTIMATOR = ML; PROCESSORS = 8; MODEL:lead BY lead21-lead30; ! specifies measurement invariance PLOT:TYPE = PLOT2; OUTPUT:TECH1 TECH8 MODINDICES(ALL);Bengt Muth en 1 factor on each level): yrij= r+BrBj+Brj+WijWij+Wrij(4)Alternative expression often used in 2-level IRT:yrij= r+rij+rij,(5)
5、ij= Bj+Wij,(6)so that is the same for between and within.Bengt Muth en MISSING = ALL (-999); CLUSTER = hosp; ANALYSIS:TYPE = TWOLEVEL; ESTIMATOR = ML; PROCESSORS = 8; MODEL:%WITHIN% leadw BY lead21-lead30* (lam1-lam10); leadw1; %BETWEEN% leadb BY lead21-lead30* (lam1-lam10); leadb; OUTPUT:TECH1 TECH
6、8 MODINDICES(ALL);Bengt Muth en VARIABLE: NAMES = y1-y4 x1 x2 w clus; WITHIN = x1 x2; BETWEEN = w; CLUSTER = clus; ANALYSIS: TYPE = TWOLEVEL RANDOM; ESTIMATOR = BAYES; PROCESSORS = 2; BITER = (1000); MODEL: %WITHIN% s1-s4 | f BY y1-y4; f1; f ON x1 x2; %BETWEEN% f ON w; f; ! defaults: s1-s4; s1-s4; P
7、LOT: TYPE = PLOT2; OUTPUT: TECH1 TECH8; Bengt Muth en f1; f ON x1 x2; %BETWEEN% fb BY y1-y4; fb ON w; f0; is the between-level defaultBengt Muth en f1; f ON x1 x2; %BETWEEN% fb BY y1-y4* (lam1-lam4); fb ON w; s1-s4*1 (lam1-lam4); Bengt Muth en rejects the non-zero variance hypothesis 51% of the time
8、BITER=100000(5000); rejects the non-zero variance hypothesis 95% of the timeBITER=100000(10000); rejects the non-zero variance hypothesis 100% of the timeConclusion: The variance component test needs good number of iterations due to estimation of tail probabilitiesPower: if we generate data with Var
9、(f)=0.05, the power to detectsignificantly non-zero variance component is 50% comparable to ML T-test of 44%Bengt Muth en f1; %BETWEEN% f; y1-y8 (v1-v8); s1-s8 (v9-v16); MODEL PRIORS: v1-v16IG(1, 0.005); OUTPUT: TECH1 TECH16;Bengt Muth en s1-s2 | f BY y1-y2; f BY y3*1; s4-s8 | f BY y4-y8; %BETWEEN%
10、f; y1-y8; s1-s8;Bengt Muth en f1; %BETWEEN% y1-y8 s1-s8; s1-s8*1 (p1-p8); fb BY y1-y8*1 (p1-p8); sigma BY s1-s8*1 (p1-p8); fb sigma;Bengt Muth en f1; %BETWEEN% f ON x; f; s1-s21 jittery-scornful; s1-s21*1 (lambda1-lambda21); sigma BY s1-s21*1 (lambda1-lambda21); sigma ON x; sigma;Bengt Muth en The r
11、andom slope s has variance on level 2 and level 3Type 2: Defined on the level 2 %BETWEEN level2% s | y ON x; The random slope s has variance on level 3 onlyThe dependent variable can be an observed Y or a factor. Thecovariate X should be specified as WITHIN= for type 1 or BETWEEN=(level2) for type 2
12、, i.e., no variation beyond the level it is used atBengt Muth en VARIABLE: NAMES = y x w z level2 level3; CLUSTER = level3 level2; WITHIN = x; BETWEEN =(level2) w (level3) z; ANALYSIS: TYPE = THREELEVEL RANDOM; MODEL: %WITHIN% s1 | y ON x; %BETWEEN level2% s2 | y ON w; s12 | s1 ON w; y WITH s1; %BET
13、WEEN level3% y ON z; s1 ON z; s2 ON z; s12 ON z; y WITH s1 s2 s12; s1 WITH s2 s12; s2 WITH s12; OUTPUT: TECH1 TECH8; Bengt Muth en VARIABLE:NAMES = hospital ward wardid nurse age gender experience stress wardtype hospsize expcon zage zgender zexperience zstress zwardtyi zhospsize zexpcon cexpcon cho
14、spsize; CLUSTER = hospital wardid; WITHIN = age gender experience; BETWEEN = (hospital) hospsize (wardid) expcon wardtype; USEVARIABLES = stress expcon age gender experience wardtype hospsize; CENTERING = GRANDMEAN(expcon hospsize); ANALYSIS:TYPE = THREELEVEL RANDOM; ESTIMATOR = MLR;Bengt Muth en %B
15、ETWEEN wardid% s | stress ON expcon; stress ON wardtype; %BETWEEN hospital% s stress ON hospsize; s; s WITH stress; OUTPUT:TECH1 TECH8; SAVEDATA:SAVE = FSCORES; FILE = fs.dat; PLOT:TYPE = PLOT2 PLOT3;Bengt Muth en VARIABLE: NAMES = u y2 y y3 x w z level2 level3; CATEGORICAL = u; CLUSTER = level3 lev
16、el2; WITHIN = x; BETWEEN = y2 (level2) w (level3) z y3; ANALYSIS: TYPE = THREELEVEL; ESTIMATOR = BAYES; PROCESSORS = 2; BITERATIONS = (1000); MODEL: %WITHIN% u ON y x; y ON x; %BETWEEN level2% u ON w y y2; y ON w; y2 ON w; y WITH y2; %BETWEEN level3% u ON y y2; y ON z; y2 ON z; y3 ON y y2; y WITH y2; u WITH y3; OUTPUT: TECH1 TECH8; Bengt Muth en VARIABLE: NAMES = y1-y6 x1 x2 w z level2 level3; CLUSTER = leve
