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Using MX for SEM analysis

Using MX for SEM analysis. Using Lisrel. Analysis of Reader Reliability in Essay Scoring Votaw's Data Tau-Equivalent Model 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

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Using MX for SEM analysis

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  1. Using MX for SEM analysis

  2. Using Lisrel Analysis of Reader Reliability in Essay Scoring Votaw's Data Tau-Equivalent Model 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 LK Esayabil EQ LX(1) - LX(4) PD OU

  3. The models in Mx A path diagram consists of four basic types of object: circles, squares, one-headed and two-headed arrows. These correspond to the following basic concepts of statistical multivariate modeling: Two types of variables: observed (in squares), non-observed (in circles) Two types of relationship between variables are possible: causal (one headed arrow) and correlational (two-headed arrow). The RAM specification(McArdle and Boker, 1990) involves three matrices: F, A and S. S is for the symmetric paths (two-headed, correlational), F is the filtering the set of observed variables out of the whole set. A is for the asymmetric paths (one-headed arrows, causal). z = F v v = A v + e ---> v = (I – A )-1 e The covariance matrix of z, Cov (z), is structured as: Cov (z) = F (I – A )-1 S ((I – A )-T F’ Instead of Cov we could just have the moment matrices, E zz’ and E vv’ . Moment Structure: S = S(q) (here S = cov (y), or Eyy’) We fit the sample moment matrix M to S = S(q)

  4. Using row data This is the file String.rec (with spaces ) !MxGui auto-generated data group data file Data Ninput=5 NObservation=15 REctangle File=string.rec Label Id True Brian David Graham 1 6.3 5 4.8 6 2 4.1 3.2 3.1 3.5 3 5.1 3.6 3.8 4.5 4 5 4.5 4.1 4.3 5 5.7 4 5.2 5 6 3.3 2.5 2.8 2.6 7 1.3 1.7 1.4 1.6 8 5.8 4.8 4.2 5.5 9 2.8 2.4 2 2.1 10 6.7 5.2 5.3 6 11 1.5 1.2 1.1 1.2 12 2.1 1.8 1.6 1.8 13 4.6 3.4 4.1 3.9 14 7.6 6 6.3 6.5 15 2.5 2.2 1.6 2 This is the file string.dat

  5. Using the graphic interface path diagram > datamap > search for the data file in raw > select variables We do factor analysis model

  6. Fitting a one factor model This is file factor.dat • Using the graphic options: • Open the pathdyagram interface • Open de file factor.dat • Select the variables on the file factor.dat • Finish drawing the model • Run and observe ... ! ! Factor.dat - example factor analysis data ! Data Ninput=5 Nobs=100 Labels verb perf matrix digit speed CMatrix 1.2 .1 1.4 .2 .3 1.5 .5 .4 .3 2.0 .3 .2 .4 .5 2.1

  7. More on using Mx

  8. File: coupon.dat An ascii xxx.dat file Data Nimput=6 Nobservations=85 CMatrix 4.389 3.792 4.410 1.935 1.855 2.385 1.454 1.453 0.989 1.914 1.087 1.309 0.841 0.961 1.480 1.623 1.701 1.175 1.279 1.220 1.971 Labels In1 In2 Beh A1 A2 A3

  9. 1: Path diagram > new diagram 2: data map 3: open file 4: opne it 5: it brings the variables in

  10. 6: highlight the variables 7: press on new

  11. Run the program

  12. Chi2 Goodness of fit df

  13. Label de Latent variables (clic twice ...)

  14. parameter estimates …

  15. Change on chi2 CI

  16. Script file File open

  17. See the output file Script file

  18. New diagram window New datamap Open new file

  19. Setting paramters to be equal across groups Overall chi2

  20. Lattin and Roberts data of adoption new technologiesp. 366 of Lattin et al. See the data file adoption.txt in RMMRS

  21. Using row data This is the file String.rec (with spaces ) !MxGui auto-generated data group data file Data Ninput=5 NObservation=15 REctangle File=string.rec Label Id True Brian David Graham 1 6.3 5 4.8 6 2 4.1 3.2 3.1 3.5 3 5.1 3.6 3.8 4.5 4 5 4.5 4.1 4.3 5 5.7 4 5.2 5 6 3.3 2.5 2.8 2.6 7 1.3 1.7 1.4 1.6 8 5.8 4.8 4.2 5.5 9 2.8 2.4 2 2.1 10 6.7 5.2 5.3 6 11 1.5 1.2 1.1 1.2 12 2.1 1.8 1.6 1.8 13 4.6 3.4 4.1 3.9 14 7.6 6 6.3 6.5 15 2.5 2.2 1.6 2 This is the file string.dat

  22. 1 2 3 4 5. highlight 6

  23. This is for modeling means

  24. Analysis of Adoption data

  25. data=read.table("E:/Albert/COURSES/RMMSS/Mx/ADOPTION.txt", header=T) names(data) [1] "ADOPt1" "ADOPt2" "VALUE1" "VALUE2" "VALUE3" "USAGE1" "USAGE2" "USAGE3" attach(data) round(cov(data, use="complete.obs"),2) ADOPt1 ADOPt2 VALUE1 VALUE2 VALUE3 USAGE1 USAGE2 USAGE3 ADOPt1 675.17 489.24 6.25 5.46 4.08 10.62 11.69 7.12 ADOPt2 489.24 994.31 4.16 4.46 3.42 16.35 17.92 12.17 VALUE1 6.25 4.16 0.95 0.37 0.45 0.16 0.19 0.12 VALUE2 5.46 4.46 0.37 0.83 0.31 0.11 0.12 0.07 VALUE3 4.08 3.42 0.45 0.31 0.86 0.13 0.18 0.05 USAGE1 10.62 16.35 0.16 0.11 0.13 0.76 0.64 0.45 USAGE2 11.69 17.92 0.19 0.12 0.18 0.64 0.92 0.55 USAGE3 7.12 12.17 0.12 0.07 0.05 0.45 0.55 0.64 Warning message: NAs introduced by coercion dim(data) [1] 188 8

  26. Adoption.dat Data Nimput=8 Nobservations=188 CMatrix 675.17 489.24 994.31 6.25 4.16 0.95 5.46 4.46 0.37 0.83 4.08 3.42 0.45 0.31 0.86 10.62 16.35 0.16 0.11 0.13 0.76 11.69 17.92 0.19 0.12 0.18 0.64 0.92 7.12 12.17 0.12 0.07 0.05 0.45 0.55 0.64 Labels ADOPt1 ADOPt2 VALUE1 VALUE2 VALUE3 USAGE1 USAGE2 USAGE3

  27. One factor model for Value

  28. Two factor model

  29. Model complert (utilitza la matriu de correlacions)

  30. Loadings of Adoption constrained Loadings of Adoption constrained.

  31. Exercices Lattin et al. pp. 383-385: 10.1 to 10.7, and specially 10.7

  32. 10.7 of p. 384 (Lettin et al. ) Impact of students’ attitude toward math and their evaluation. Students in the program were surveyed Twice about their attitude (once at the beginning of the fall semester and again at the beginning of the srping semester). The researcher has also access to the score of a graduate-level student attitude test from the program application. The researcher used the following three questions to assess attitude toward math (each measured on a seven point semantic differntial scale). X1 Nervous-Confident X2 Capable-Inept X3 Angry-Happy XX1 to XX3, the same on time 2 The researcher captured the student’s evaluation of the quantitative course with the following Three measures (all measured on a sevent point Likert scale from 7 = strongly agree to 1 = strongly disagree ) Y1 I will be able to use what I learned Y2 The subject matter of this course was not relevant to me Y3 This was a great course Tscore Apptitude Test Score (from the program application) Research Question: Test the hypothesis that there is no effect of attitude toward math on student evaluations of the new quantitative course, controlling for the effect of student aptitude. What do you conclude ?.

  33. data= read.table("E:/Albert/COURSES/RMMSS/MATH_ATTITUDElabels.txt", header=T)> attach(data)> names(data) [1] "ID" "X1" "X2" "X3" "XX1" "XX2" "XX3" "Y1" [9] "Y2" "Y3" "Tscore" pairs(data[,2:10]) dim(data)[1] 141 11> round(cor(data[,2:11]),2) X1 X2 X3 XX1 XX2 XX3 Y1 Y2 Y3 TscoreX1 1.00 -0.65 0.61 0.86 -0.62 0.54 0.33 -0.20 0.28 0.15X2 -0.65 1.00 -0.56 -0.60 0.84 -0.49 -0.22 0.16 -0.18 -0.14X3 0.61 -0.56 1.00 0.59 -0.54 0.86 0.25 -0.17 0.28 0.04XX1 0.86 -0.60 0.59 1.00 -0.78 0.73 0.24 -0.17 0.26 0.08XX2 -0.62 0.84 -0.54 -0.78 1.00 -0.70 -0.18 0.15 -0.20 -0.12XX3 0.54 -0.49 0.86 0.73 -0.70 1.00 0.18 -0.14 0.25 0.03Y1 0.33 -0.22 0.25 0.24 -0.18 0.18 1.00 -0.58 0.62 0.29Y2 -0.20 0.16 -0.17 -0.17 0.15 -0.14 -0.58 1.00 -0.50 -0.15Y3 0.28 -0.18 0.28 0.26 -0.20 0.25 0.62 -0.50 1.00 0.19Tscore 0.15 -0.14 0.04 0.08 -0.12 0.03 0.29 -0.15 0.19 1.00> round(cov(data[,2:11]),2) X1 X2 X3 XX1 XX2 XX3 Y1 Y2 Y3 TscoreX1 2.62 -1.67 1.60 2.47 -1.77 1.59 0.85 -0.47 0.66 12.53X2 -1.67 2.51 -1.43 -1.69 2.36 -1.42 -0.57 0.37 -0.42 -11.62X3 1.60 -1.43 2.64 1.69 -1.56 2.55 0.65 -0.40 0.66 3.72XX1 2.47 -1.69 1.69 3.16 -2.48 2.37 0.67 -0.43 0.67 7.71XX2 -1.77 2.36 -1.56 -2.48 3.16 -2.30 -0.50 0.38 -0.52 -11.77XX3 1.59 -1.42 2.55 2.37 -2.30 3.36 0.52 -0.38 0.68 2.89Y1 0.85 -0.57 0.65 0.67 -0.50 0.52 2.56 -1.36 1.44 24.25Y2 -0.47 0.37 -0.40 -0.43 0.38 -0.38 -1.36 2.10 -1.04 -11.59Y3 0.66 -0.42 0.66 0.67 -0.52 0.68 1.44 -1.04 2.09 14.44Tscore 12.53 -11.62 3.72 7.71 -11.77 2.89 24.25 -11.59 14.44 2808.07>>

  34. File: math.dat An ascii xxx.dat file Data Nimput=10 Nobservations=141 CMatrix FULL 2.62 -1.67 1.60 2.47 -1.77 1.59 0.85 -0.47 0.66 12.53 -1.67 2.51 -1.43 -1.69 2.36 -1.42 -0.57 0.37 -0.42 -11.62 1.60 -1.43 2.64 1.69 -1.56 2.55 0.65 -0.40 0.66 3.72 2.47 -1.69 1.69 3.16 -2.48 2.37 0.67 -0.43 0.67 7.71 -1.77 2.36 -1.56 -2.48 3.16 -2.30 -0.50 0.38 -0.52 -11.77 1.59 -1.42 2.55 2.37 -2.30 3.36 0.52 -0.38 0.68 2.89 0.85 -0.57 0.65 0.67 -0.50 0.52 2.56 -1.36 1.44 24.25 -0.47 0.37 -0.40 -0.43 0.38 -0.38 -1.36 2.10 -1.04 -11.59 0.66 -0.42 0.66 0.67 -0.52 0.68 1.44 -1.04 2.09 14.44 12.53 -11.62 3.72 7.71 -11.77 2.89 24.25 -11.59 14.44 2808.07 Labels X1 X2 X3 XX1 XX2 XX3 Y1 Y2 Y3 Tscore X1 Nervous-Confident X2 Capable-Inept X3 Angry-Happy XX1 to XX3, the same on time 2 On the scale 7 = strongly agree to 1 = strongly disagree Y1 I will be able to use what I learned Y2 The subject matter of this course was not relevant to me Y3 This was a great course Tscore Apptitude Test Score

  35. One factor model

  36. The costumer Orientatin of Service Workers: Personality Trait Effects on Self and Supervisor Performance Ratings Tom J. Brown et al. May 2000 (forthcoming, Journal of Marketing Research)

  37. The items

  38. Sample moments

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