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SEM BASIC MODELS

SEM BASIC MODELS. Regression Model. V3 = * V1 + *V2+ D. V1. D. *. V3. *. *. V2. Regression with error-in-variables. Ex. 3.1.2 of Fuller (1987) Data from a sample of Iowa farm operators Y = ln (farm size) X1 = ln ( # years experience ) X2 = ln (# years education )

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SEM BASIC MODELS

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  1. SEM BASIC MODELS

  2. Regression Model V3 = *V1 + *V2+ D V1 D * V3 * * V2

  3. Regression with error-in-variables Ex. 3.1.2 of Fuller (1987) Data from a sample of Iowa farm operators Y = ln (farm size) X1 = ln ( # years experience ) X2 = ln (# years education ) (to protect confidentiality, random error was added to each variable)

  4. Regression with error-in-variables * V1 D3 E1 F1 * F3 * V2 * E2 * F2 * V3 E3 F3 = *F1 + *F2 + D3 V1 = F1 + E1 V2 = F2 + E2 V3 = F3 + E3 E1 = .0997; E2 = .2013; E3 = .1808; Coeficientes de fiabilidad son .80, .83 y .89 respectivamente

  5. N=176 Regression equation

  6. Regression with error-in-variables /TITLE MODELO DE REGRESION CON ERROR EN LAS VARIABLES /SPECIFICATIONS CAS=176; VAR=3; ME=ML; /LABELS V1=TAMANO; V2=EXPER; V3=EDUCAC; F1=TAM; F2=EXP; F3=EDU; /EQUATIONS V1 = F1+ E1; V2 = F2+ E2; V3 = F3+ E3; F1=*F2+*F3+D1; /VARIANCES F2 TO F3 = *; D1=*; E1 = 0.0997; E2 = 0.2013; E3 = 0.1808; /COVARIANCES F2,F3 = *; /MATRIX .9148 .2129 1.006 .0714 -.449 1.039 /PRINT DIG=4; /END

  7. D3 * V1 V3 * * D4 V2 * V4 Path analysis model V3 = *V1 + *V2 + D3 V4 = *V1 + *V2 + D4 *

  8. Simultaneous equations Education development, Sewell, Haller & Ohlendorf (1970) sample of n = 3500 where: Y1 = academic performance (AP), Y2 = significant influences of others(SO), Y3 = educational aspirations (EA), X1 = mental ability (MA), X2 = socioeconomic status (SES).

  9. u3 e2 y2 u2 Y1 X1 Y3 X2 Y2 Model: df = chi2=7.14. Without introducing measurement error on Y2, chi2 is 186.39 with3 df, so …

  10. Path analysis model //TITLE modified Sewell et al (1970) model /SPECIFICATIONS CAS=3500; VAR=5; ME=ML; MA=COR; ANAL=COR; /LABELS V1=HABMENT; V2=ESTATSOC; V3=EXACAD; V4=INFOTROS; V5=ASPEDUC; /EQUATIONS V3 =*V1 +D1; F1 =*V1+*V2+*V3 +D2; V5 = *V3+*F1 +D3; V4=F1+E1; /VARIANCES E1=*; V1 TO V2 = *; D1 TO D3 = *; /COVARIANCES V1 TO V2 = *; /MATRIX 1.000 .288 1.000 .589 .194 1.000 .438 .359 .473 1.000 .418 .380 .459 .611 1.000 /PRINT DIG=3; /END

  11. Mimic model Joreskog & Goldberger, JASA (1979) y =social participation X1 = Income X2 = Occupation X3 = Education Y1= Church attendance Y2 = Membership Y3 = Frieds Seen X1 Y1 u1 b1 l1 b2 l2 X2 y Y2 u2 l3 b3 X3 Y3 u3 e

  12. V1 V4 E2 * * * * V2 F1 V5 E5 * * V3 V6 E6 D1 Mimic model F1 = *V1 + *V2 + *V3 + D V4 = *F1 + E4 V5 = *F1 + E5 V6 = *F1 + E6 * * *

  13. ML estimates: 6 overidentifying restrictions. The corresponding chi2 is 12.36 with “P-VALUE” 0.052.

  14. Mimic model /TITLE Modelo MIMIC /SPECIFICATIONS VARIABLES=6; CASES=530; METHODS=ML; MATRIX=CORRELATION; /LABELS V1 = Income; V2 = Occupa; V3 = Educat; V4 = Church; V5 = Afiliat ; V6 = Friends; /EQUATIONS V4 = 1F1 + E4; V5 = *F1 + E5; V6 = *F1 + E6; F1 = *V1 + *V2 + *V3 + D1; /VARIANCES V1 TO V3 = *; E4 TO E6 = *; D1 = *; /COVARIANCES V2 , V1 = *; V3 , V1 = *; V3 , V2 = *; /MATRIX 1.000 0.304 1.000 0.305 0.344 1.000 0.100 0.156 0.158 1.000 0.284 0.192 0.324 0.360 1.000 0.176 0.136 0.226 0.210 0.265 1.000 /LMTEST /WTEST /PRINT

  15. Panel data xta = gt + bx(t-1)a + la + mta Xta = xta + vta t = 1,2, ..., T a = 1,2,..., N Anderson (1986) xta budget of household a at time t la individual (unobserved) characteristic of household a

  16. Panel data E2 E1 E3 E4 E5 ET V1 V2 V3 V4 V5 VT …. 1 1 1 1 1 1 * * * * * …. * F1 F2 F3 F4 F5 FT D2 D3 D4 D5 DT 1 1 1 1 1 1 F0 In a stationary process, Var(F1)=[Var(D) + Var F0 ]/(1-b)

  17. Factor analysis (Spearman, 1904) Variables CLASSIC = V1 FRENCH = V2 ENGLISH = V3 MATH = V4 DISCRIM = V5 MUSIC = V6 Correlation matrix 1 .83 1 .78 .67 1 .70 .64 .64 1 .66 .65 .54 .45 1 .63 .57 .51 .51 .40 1 cases = 23;

  18. Single-Factor Model * * * * * * V1 V2 V3 V4 V5 V6 * * * * * * F1

  19. EQS code for a factor model RESIDUAL COVARIANCE MATRIX (S-SIGMA) : CLASSIC FRENCH ENGLISH MATH DISCRIM V 1 V 2 V 3 V 4 V 5 CLASSIC V 1 0.000 FRENCH V 2 -0.001 0.000 ENGLISH V 3 0.005 -0.029 0.000 MATH V 4 -0.006 0.003 0.046 0.000 DISCRIM V 5 -0.001 0.054 -0.015 -0.056 0.000 MUSIC V 6 0.003 0.005 -0.017 0.030 -0.049 MUSIC V 6 MUSIC V 6 0.000 CHI-SQUARE = 1.663 BASED ON 9 DEGREES OF FREEDOM PROBABILITY VALUE FOR THE CHI-SQUARE STATISTIC IS 0.99575 THE NORMAL THEORY RLS CHI-SQUARE FOR THIS ML SOLUTION IS 1.648 .

  20. Single-Factor Model Loadings’ estimates , s.e. and z-test statistics CLASSIC =V1 = .960*F1 +1.000 E1 .160 6.019 FRENCH =V2 = .866*F1 +1.000 E2 .171 5.049 ENGLISH =V3 = .807*F1 +1.000 E3 .178 4.529 MATH =V4 = .736*F1 +1.000 E4 .186 3.964 DISCRIM =V5 = .688*F1 +1.000 E5 .190 3.621 MUSIC =V6 = .653*F1 +1.000 E6 .193 3.382 Unique factors E1 -CLASSIC .078*I .064 I 1.224 I I E2 -FRENCH .251*I .093 I 2.695 I I E3 -ENGLISH .349*I .118 I 2.958 I I E4 - MATH .459*I .148 I 3.100 I I E5 -DISCRIM .527*I .167 I 3.155 I I E6 -MUSIC .574*I .180 I 3.184 I I

  21. Single-Factor Model STANDARDIZED SOLUTION: CLASSIC =V1 = .960*F1 + .279 E1 FRENCH =V2 = .866*F1 + .501 E2 ENGLISH =V3 = .807*F1 + .591 E3 MATH =V4 = .736*F1 + .677 E4 DISCRIM =V5 = .688*F1 + .726 E5 MUSIC =V6 = .653*F1 + .758 E6

  22. Factor analysis Vi = l Fi + Ei Var Fi = 1 Var Ei = f F1 F2 V1 V2 V3 V4 E1 E2 E3 E4

  23. Lisrel example Analysis of Reader Reliability in Essay Scoring Analysis of Reader Reliability in Essay Scoring Votaw's Data Congeneric model estimated by ML DA NI=4 NO=126 LA ORIGPRT1 WRITCOPY CARBCOPY ORIGPRT2 CM 25.0704 12.4363 28.2021 11.7257 9.2281 22.7390 20.7510 11.9732 12.0692 21.8707 MO NX=4 NK=1 LX=FR PH=ST !EQ TD(1) - TD(4) !EQ LX(1) - LX(4)LK Esayabil PD OU

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