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

LK

Esayabil

EQ LX(1) - LX(4)

PD

OU

The models in MxA 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: = ( (here = cov (y), or Eyy’) We fit the sample moment matrix M to = (

Using row data

!MxGui auto-generated data group data file

Data Ninput=5 NObservation=15

REctangle File=string.rec

Label

Id True Brian David Graham

This is the file string.dat

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 fileString.rec (with spaces )

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

Brian David Graham

G L

0.06

I1.38 M

3.43

0.14

J1.53

N3.43

0.02

K1.73

O3.77

1.00

Appears OK -2LnLGroup Fit: 77.2941

Fit 77.294Probability 0.000

AIC 0.000RMSEA 0.000

Degrees of freedom 36Free parameters 9

Observed Statistics 45Constraints 0

Fitting a one factor modelUsing the graphic options:

• Open the path dyagram 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=100Labels 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

This is file factor.dat

0.95

verb

1.23

perf

1.30

matrix

1.23

digit

1.73

speed

1.00

L1

N10.50

O10.41

P10.45

Q10.88

R10.61

Appears OK ML ChiSqGroup Fit: 3.75358

Fits 3.754 (5.000, 12.178)Probability 0.585

AIC -6.246 (-5.000, 2.178)RMSEA 0.000 (0.000, 0.120)

Degrees of freedom 5Free parameters 10

Observed Statistics 15Constraints 0

More on using Mx

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

File: coupon.dat

1: Path diagram > new diagram

2: data map 3: open file

4: opne it

5: it brings the variables in

6: highlight the variables

7: press on new

Run the program

Chi2 Goodness of fit

df

Label de Latent variables(clic twice ...)

parameter estimates …

CI

Change on chi2

Script file

File open

Script file

See the output file

New diagramwindow

Open new file

New datamap

Setting paramters to be equal across groups

Overall chi2

Lattin and Roberts data of adoption new technologies

p. 366 of Lattin et al.

See the data file adoption.txt in RMMRS

Using row data

!MxGui auto-generated data group data file

Data Ninput=5 NObservation=15

REctangle File=string.rec

Label

Id True Brian David Graham

This is the file string.dat

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 fileString.rec (with spaces )

1 2

3

4

5. highlight

6

This is for modeling means

Analysis of Adoption data

 

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

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

Adoption.dat

One factor model for Value

Two factor model

Model complert (utilitza la matriu de correlacions)

Loadings of Adoption constrained.

Loadings of Adoption constrained

Exercices

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

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-ConfidentX2 Capable-IneptX3 Angry-HappyXX1 to XX3, the same on time 2The 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 learnedY2 The subject matter of this course was not relevant to meY3 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 ?.

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>>

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

File: math.dat

X1 Nervous-ConfidentX2 Capable-IneptX3 Angry-HappyXX1 to XX3, the same on time 2On the scale 7 = strongly agree to 1 = strongly disagree Y1 I will be able to use what I learnedY2 The subject matter of this course was not relevant to meY3 This was a great course Tscore Apptitude Test Score

One factor model

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)

The items Measures Used in Analyses

Introversion (9-point, "never-always;" = .86) Conscientiousness (9-point, "never-always;" = .73)Feel bashful more than others. Precise.Quiet when with people. Organized.Shy. Sloppy. (R)

Orderly.Instability (9-point, "never-always;" = .88)Moody more than others. Openness (9-point, "never-always;" = .83)Temperamental. Frequently feel highly creative.Envious. Imaginative.Emotions go way up and down. Appreciate art.Testy more than others. Find novel solutions.

More original than others.

Agreeability (9-point, "never-always;" = .85) Activity (9-point, "never-always;" = .79)Tender hearted with others. Have a hard time keeping still.Sympathetic. Extremely active in my daily life.Kind to others. Have a hard time sitting around.

Customer Orientation (reliability for the linear composite = .92)Enjoyment Dimension (9-point, "strongly disagree-strongly agree;" = .88)I find it easy to smile at each of my customers.I enjoy remembering my customers' names.It comes naturally to have empathy for my customers.I enjoy responding quickly to my customers' requests.I get satisfaction from making my customers happy.I really enjoy serving my customers.

Needs Dimension (9-point, "strongly disagree-strongly agree;" = .87)I try to help customers achieve their goals.I achieve my own goals by satisfying customers.I get customers to talk about their service needs with me.I take a problem solving approach with my customers.I keep the best interests of the customer in mind.I am able to answer a customer's questions correctly.

Performance Evaluations (7-point, "among the worst in the company-among the best in the company")Overall quantity of work performed.Overall quality of work performed.(Identical scales used for self and supervisor performance evaluation)

Sample moments

Table 1Descriptive Statistics and Bivariate Correlations

#Items

CoefficientAlpha

{INCRUSTA

RUnknown}

s.d. (X1) (X2) (X3) (X4) (X5) (X6) (Y1) (Y2) (Y3) (Y4) (Y5) (Y6)

) 3 .86 3.39 1.82) 5 .88 3.90 1.79 .41) 3 .85 7.04 1.51 -.04 -.21) 4 .73 6.52 1.35 -.10 -.08 .21) 5 .83 6.20 1.53 -.07 .06 .26 .11) 3 .79 5.71 1.80 -.18 -.01 .16 .18 .30) 6 .88 6.87 1.47 -.23 -.30 .41 .20 .16 .28) 6 .87 7.06 1.33 -.16 -.15 .32 .19 .24 .29 .65) 1 NA 5.64 1.02 -.10 -.07 .16 .12 .13 .17 .35 .31) 1 NA 5.79 0.96 -.13 -.21 .20 .23 .16 .13 .38 .32 .72) 1 NA 5.41 1.23 -.07 -.06 -.07 .17 -.08 .01 .08 .10 .23 .28) 1 NA 5.39 1.27 -.06 -.08 -.07 .19 -.11 -.04 .09 .12 .22 .28 .86

otes: n = 249; mean scores used for all multi-item scales; all 9-point scales except Y3 – Y6 (7-point).

Figure 1Basic Models Tested in Study

Conscientiousness

(a) Full Mediation Model

Introversion

Instability

Agreeability

Openness

Activity

Introversion

Instability

Agreeability

Conscientiousness

Openness

Activity

(b) Partial Mediation Model

PerformanceRatings(Self )

PerformanceRatings

(Supervisor)

PerformanceRatings(Self )

PerformanceRatings

(Supervisor)

CustomerOrientation

CustomerOrientation