Jason T. Newsom, Richard N. Jones, & Scott M. Hofer.

Longitudinal data analysis: A practical guide for researchers in aging, health, and social sciences

 

CHAPTER 9

 

Jones R.

 

 

Table 9.1 Results of Unconditional and Conditional Latent Growth Curve Models of

Change in Mini-Mental State Examination Performance in the Hispanic EPESE

 

Mm =  Mini-Mental state examination performance

cBage  = centered age

cgrs23007  = centered gender

ceds23018 = centered education

cras23008 = centered born in US

civs23483 = centered Spanish interview

 

 

UNCONDITIONAL MODEL

 

 

 

Analysis Summary
Date and Time

Date: Thursday, March 31, 2011

Time: 4:23:15 PM

Title

chpt9unc amos: Thursday, March 31, 2011 4:23 PM

Groups
Group number 1 (Group number 1)
Notes for Group (Group number 1)

The model is recursive.

Sample size = 2942

Variable Summary (Group number 1)
Your model contains the following variables (Group number 1)

Observed, endogenous variables

MM0

MM1

MM2

MM3

MM4

MM5

mm6

mm7

mm8

Unobserved, exogenous variables

ICEPT

SLOPE

E1

E2

E3

E4

E5

E6

E7

E8

E9

Variable counts (Group number 1)

Number of variables in your model:

20

Number of observed variables:

9

Number of unobserved variables:

11

Number of exogenous variables:

11

Number of endogenous variables:

9

Parameter summary (Group number 1)

 

Weights

Covariances

Variances

Means

Intercepts

Total

Fixed

27

0

0

0

0

27

Labeled

0

0

9

0

0

9

Unlabeled

0

1

2

2

0

5

Total

27

1

11

2

0

41

Models
Default model (Default model)
Notes for Model (Default model)
Computation of degrees of freedom (Default model)

Number of distinct sample moments:

54

Number of distinct parameters to be estimated:

6

Degrees of freedom (54 - 6):

48

Result (Default model)

Minimum was achieved

Function of log likelihood = 39289.117

Number of parameters = 6

Group number 1 (Group number 1 - Default model)
Estimates (Group number 1 - Default model)
Scalar Estimates (Group number 1 - Default model)
Maximum Likelihood Estimates
Regression Weights: (Group number 1 - Default model)

 

 

 

Estimate

S.E.

C.R.

P

Label

MM0

<---

ICEPT

1.000

 

 

 

 

MM0

<---

SLOPE

.000

 

 

 

 

MM1

<---

ICEPT

1.000

 

 

 

 

MM1

<---

SLOPE

1.000

 

 

 

 

MM2

<---

ICEPT

1.000

 

 

 

 

MM2

<---

SLOPE

2.000

 

 

 

 

MM3

<---

ICEPT

1.000

 

 

 

 

MM3

<---

SLOPE

3.000

 

 

 

 

MM4

<---

ICEPT

1.000

 

 

 

 

MM4

<---

SLOPE

4.000

 

 

 

 

MM5

<---

ICEPT

1.000

 

 

 

 

MM5

<---

SLOPE

5.000

 

 

 

 

mm6

<---

SLOPE

6.000

 

 

 

 

mm7

<---

SLOPE

7.000

 

 

 

 

mm8

<---

SLOPE

8.000

 

 

 

 

mm6

<---

ICEPT

1.000

 

 

 

 

mm7

<---

ICEPT

1.000

 

 

 

 

mm8

<---

ICEPT

1.000

 

 

 

 

Standardized Regression Weights: (Group number 1 - Default model)

 

 

 

Estimate

MM0

<---

ICEPT

.691

MM0

<---

SLOPE

.000

MM1

<---

ICEPT

.660

MM1

<---

SLOPE

.112

MM2

<---

ICEPT

.626

MM2

<---

SLOPE

.213

MM3

<---

ICEPT

.590

MM3

<---

SLOPE

.301

MM4

<---

ICEPT

.555

MM4

<---

SLOPE

.378

MM5

<---

ICEPT

.522

MM5

<---

SLOPE

.443

mm6

<---

SLOPE

.500

mm7

<---

SLOPE

.548

mm8

<---

SLOPE

.590

mm6

<---

ICEPT

.490

mm7

<---

ICEPT

.461

mm8

<---

ICEPT

.434

Means: (Group number 1 - Default model)

 

 

 

Estimate

S.E.

C.R.

P

Label

ICEPT

 

 

24.387

.090

271.125

***

 

SLOPE

 

 

-.681

.022

-31.571

***

 

Covariances: (Group number 1 - Default model)

 

 

 

Estimate

S.E.

C.R.

P

Label

ICEPT

<-->

SLOPE

1.121

.112

10.007

***

 

Correlations: (Group number 1 - Default model)

 

 

 

Estimate

ICEPT

<-->

SLOPE

.505

Variances: (Group number 1 - Default model)

 

 

 

Estimate

S.E.

C.R.

P

Label

ICEPT

 

 

13.054

.665

19.619

***

 

SLOPE

 

 

.377

.032

11.845

***

 

E1

 

 

14.298

.336

42.545

***

V

E2

 

 

14.298

.336

42.545

***

V

E3

 

 

14.298

.336

42.545

***

V

E4

 

 

14.298

.336

42.545

***

V

E5

 

 

14.298

.336

42.545

***

V

E6

 

 

14.298

.336

42.545

***

V

E7

 

 

14.298

.336

42.545

***

V

E9

 

 

14.298

.336

42.545

***

V

E8

 

 

14.298

.336

42.545

***

V

Minimization History (Default model)

Iteration

 

Negative
eigenvalues

Condition #

Smallest
eigenvalue

Diameter

F

NTries

Ratio

0

e

1

 

-.178

9999.000

96282.393

0

9999.000

1

e*

3

 

-.930

1.268

46408.431

14

.717

2

e

3

 

-2.832

.383

43094.619

5

.660

3

e

1

 

-1.284

.123

41608.650

5

.760

4

e

1

 

-.132

.090

41111.767

5

.715

5

e*

0

24910.787

 

.245

40036.034

6

.830

6

e

0

1741.184

 

.702

39722.978

3

.000

7

e

0

859.598

 

.204

39381.903

1

1.218

8

e

0

867.571

 

.080

39299.075

1

1.177

9

e

0

862.529

 

.023

39289.388

1

1.099

10

e

0

844.135

 

.002

39289.118

1

1.022

11

e

0

834.756

 

.000

39289.117

1

1.001

Model Fit Summary

The saturated model was not fitted to the data of at least one group. For this reason, only the 'function of log likelihood', AIC and BCC are reported. The likelihood ratio chi square statistic and other fit measures are not reported.

CMIN

Model

NPAR

CMIN

Default model

6

39289.117

AIC

Model

AIC

BCC

BIC

CAIC

Default model

39301.117

39301.158

 

 

Execution time summary

Minimization:

.047

Miscellaneous:

.296

Bootstrap:

.000

Total:

.343

 

 


 Table 9.1 Results of Unconditional and Conditional Latent Growth Curve Models of

Change in Mini-Mental State Examination Performance in the Hispanic EPESE

 

 

 

 

CONDITIONAL MODEL

 

 

 

Output from this model differs somewhat from the Mplus and Lisrel output because of minor differences in how missing data is estimated with FIML. Amos did not print the chi-square for the model because of low covariance coverage of missing data.

C:\jason\amos\longitudinal book\jones\chpt9con amos.amw

Analysis Summary
Date and Time

Date: Thursday, March 31, 2011

Time: 4:13:55 PM

Title

chpt9con amos: Thursday, March 31, 2011 4:13 PM

Groups
Group number 1 (Group number 1)
Notes for Group (Group number 1)

The model is recursive.

Sample size = 2942

Variable Summary (Group number 1)
Your model contains the following variables (Group number 1)

Observed, endogenous variables

MM0

MM1

MM2

MM3

MM4

MM5

mm6

mm7

mm8

Observed, exogenous variables

grs23007

eds23018

ivs23483

Bage

ras23008

Unobserved, endogenous variables

ICEPT

SLOPE

Unobserved, exogenous variables

E1

E2

E3

E4

E5

E6

E7

E8

E9

d1

d2

Variable counts (Group number 1)

Number of variables in your model:

27

Number of observed variables:

14

Number of unobserved variables:

13

Number of exogenous variables:

16

Number of endogenous variables:

11

Parameter summary (Group number 1)

 

Weights

Covariances

Variances

Means

Intercepts

Total

Fixed

29

0

0

0

0

29

Labeled

0

0

0

0

0

0

Unlabeled

10

11

16

0

2

39

Total

39

11

16

0

2

68

Models
Default model (Default model)
Notes for Model (Default model)
Computation of degrees of freedom (Default model)

Number of distinct sample moments:

119

Number of distinct parameters to be estimated:

39

Degrees of freedom (119 - 39):

80

Result (Default model)

Minimum was achieved

Function of log likelihood = 57513.708

Number of parameters = 39

Group number 1 (Group number 1 - Default model)
Estimates (Group number 1 - Default model)
Scalar Estimates (Group number 1 - Default model)
Maximum Likelihood Estimates
Regression Weights: (Group number 1 - Default model)

 

 

 

Estimate

S.E.

C.R.

P

Label

ICEPT

<---

grs23007

.024

.158

.151

.880

 

SLOPE

<---

grs23007

.003

.041

.080

.936

 

ICEPT

<---

eds23018

.496

.022

22.571

***

 

ICEPT

<---

ivs23483

.543

.207

2.627

.009

 

ICEPT

<---

Bage

-.191

.012

-16.030

***

 

ICEPT

<---

ras23008

-.042

.166

-.254

.799

 

SLOPE

<---

eds23018

-.005

.006

-.935

.350

 

SLOPE

<---

ivs23483

.038

.053

.711

.477

 

SLOPE

<---

Bage

-.043

.003

-13.996

***

 

SLOPE

<---

ras23008

.047

.043

1.092

.275

 

MM0

<---

ICEPT

1.000

 

 

 

 

MM0

<---

SLOPE

.000

 

 

 

 

MM1

<---

ICEPT

1.000

 

 

 

 

MM1

<---

SLOPE

1.000

 

 

 

 

MM2

<---

ICEPT

1.000

 

 

 

 

MM2

<---

SLOPE

2.000

 

 

 

 

MM3

<---

ICEPT

1.000

 

 

 

 

MM3

<---

SLOPE

3.000

 

 

 

 

MM4

<---

ICEPT

1.000

 

 

 

 

MM4

<---

SLOPE

4.000

 

 

 

 

MM5

<---

ICEPT

1.000

 

 

 

 

MM5

<---

SLOPE

5.000

 

 

 

 

mm6

<---

SLOPE

6.000

 

 

 

 

mm7

<---

SLOPE

7.000

 

 

 

 

mm8

<---

SLOPE

8.000

 

 

 

 

mm6

<---

ICEPT

1.000

 

 

 

 

mm7

<---

ICEPT

1.000

 

 

 

 

mm8

<---

ICEPT

1.000

 

 

 

 

Standardized Regression Weights: (Group number 1 - Default model)

 

 

 

Estimate

ICEPT

<---

grs23007

.003

SLOPE

<---

grs23007

.003

ICEPT

<---

eds23018

.492

ICEPT

<---

ivs23483

.057

ICEPT

<---

Bage

-.326

ICEPT

<---

ras23008

-.005

SLOPE

<---

eds23018

-.034

SLOPE

<---

ivs23483

.026

SLOPE

<---

Bage

-.475

SLOPE

<---

ras23008

.038

MM0

<---

ICEPT

.763

MM0

<---

SLOPE

.000

MM1

<---

ICEPT

.728

MM1

<---

SLOPE

.113

MM2

<---

ICEPT

.706

MM2

<---

SLOPE

.218

MM3

<---

ICEPT

.589

MM3

<---

SLOPE

.273

MM4

<---

ICEPT

.549

MM4

<---

SLOPE

.339

MM5

<---

ICEPT

.536

MM5

<---

SLOPE

.414

mm6

<---

SLOPE

.480

mm7

<---

SLOPE

.548

mm8

<---

SLOPE

.571

mm6

<---

ICEPT

.517

mm7

<---

ICEPT

.507

mm8

<---

ICEPT

.462

Intercepts: (Group number 1 - Default model)

 

 

 

Estimate

S.E.

C.R.

P

Label

ICEPT

 

 

24.428

.078

312.651

***

 

SLOPE

 

 

-.693

.020

-34.377

***

 

Covariances: (Group number 1 - Default model)

 

 

 

Estimate

S.E.

C.R.

P

Label

grs23007

<-->

eds23018

-.059

.036

-1.666

.096

 

grs23007

<-->

ivs23483

.005

.004

1.321

.187

 

grs23007

<-->

Bage

.013

.061

.210

.833

 

eds23018

<-->

ivs23483

-.556

.031

-17.678

***

 

ras23008

<-->

grs23007

.004

.005

.961

.336

 

ivs23483

<-->

Bage

.095

.051

1.870

.061

 

eds23018

<-->

Bage

-4.074

.488

-8.349

***

 

ras23008

<-->

Bage

-.411

.062

-6.661

***

 

ras23008

<-->

eds23018

.431

.037

11.752

***

 

ras23008

<-->

ivs23483

-.055

.004

-14.112

***

 

d1

<-->

d2

.402

.107

3.777

***

 

Correlations: (Group number 1 - Default model)

 

 

 

Estimate

grs23007

<-->

eds23018

-.031

grs23007

<-->

ivs23483

.024

grs23007

<-->

Bage

.004

eds23018

<-->

ivs23483

-.347

ras23008

<-->

grs23007

.018

ivs23483

<-->

Bage

.035

eds23018

<-->

Bage

-.157

ras23008

<-->

Bage

-.124

ras23008

<-->

eds23018

.223

ras23008

<-->

ivs23483

-.270

d1

<-->

d2

.245

Variances: (Group number 1 - Default model)

 

 

 

Estimate

S.E.

C.R.

P

Label

grs23007

 

 

.244

.006

38.347

***

 

eds23018

 

 

15.111

.397

38.089

***

 

ivs23483

 

 

.170

.004

38.347

***

 

Bage

 

 

44.765

1.167

38.347

***

 

ras23008

 

 

.246

.006

38.334

***

 

d1

 

 

9.509

.569

16.699

***

 

d2

 

 

.283

.032

8.828

***

 

E1

 

 

11.032

.552

19.999

***

 

E2

 

 

11.583

1.313

8.823

***

 

E3

 

 

10.667

.504

21.151

***

 

E4

 

 

20.717

2.549

8.129

***

 

E5

 

 

23.178

6.904

3.357

***

 

E6

 

 

20.686

.999

20.712

***

 

E7

 

 

19.035

1.929

9.867

***

 

E8

 

 

14.998

1.209

12.401

***

 

E9

 

 

20.032

2.892

6.928

***

 

Minimization History (Default model)

Iteration

 

Negative
eigenvalues

Condition #

Smallest
eigenvalue

Diameter

F

NTries

Ratio

0

e

3

 

-.116

9999.000

116727.749

0

9999.000

1

e*

10

 

-.921

1.284

66658.862

14

.707

2

e

11

 

-2.642

.305

63067.396

5

.777

3

e*

3

 

-.198

.238

61370.672

5

.738

4

e

3

 

-.090

.093

60493.438

5

.750

5

e

2

 

-.014

.335

59416.523

8

.861

6

e

0

1668579.660

 

.503

58253.263

5

.964

7

e

0

29387.425

 

1.621

57918.551

4

.000

8

e

0

4514.720

 

.338

57656.980

1

.988

9

e

0

4651.941

 

.100

57558.468

1

1.211

10

e

0

5484.413

 

.064

57531.628

1

1.256

11

e

0

5569.580

 

.077

57520.279

1

1.288

12

e

0

7109.571

 

.086

57515.408

1

1.259

13

e

0

13943.510

 

.077

57513.933

1

1.201

14

e

0

19875.663

 

.043

57513.716

1

1.110

15

e

0

21556.448

 

.010

57513.708

1

1.026

16

e

0

21700.112

 

.000

57513.708

1

1.001

Model Fit Summary

The saturated model was not fitted to the data of at least one group. For this reason, only the 'function of log likelihood', AIC and BCC are reported. The likelihood ratio chi square statistic and other fit measures are not reported.

CMIN

Model

NPAR

CMIN

Default model

39

57513.708

AIC

Model

AIC

BCC

BIC

CAIC

Default model

57591.708

57592.108

 

 

Execution time summary

Minimization:

.156

Miscellaneous:

.452

Bootstrap:

.000

Total:

.608