Longitudinal data
description
Transcript of Longitudinal data
![Page 1: Longitudinal data](https://reader036.fdocuments.in/reader036/viewer/2022081501/568147f5550346895db52af6/html5/thumbnails/1.jpg)
Longitudinal data
• Used commonly in developmental psychology, but also in other fields
• Longitudinal data are very useful for determining trajectories of functioning (i.e., depression over 5 years)
• Also useful for determining causal relations
![Page 2: Longitudinal data](https://reader036.fdocuments.in/reader036/viewer/2022081501/568147f5550346895db52af6/html5/thumbnails/2.jpg)
My favorite example
StressPsycho.
adaptation-.58**
Note. These data are typically obtained in one point of time,i.e., they are concurrent. Can we draw the arrow as we have here?
![Page 3: Longitudinal data](https://reader036.fdocuments.in/reader036/viewer/2022081501/568147f5550346895db52af6/html5/thumbnails/3.jpg)
Correlation is not causation!(Have we heard that before?)
Stress
Psycho.adaptation
r = -.58**
What is the direction of causation, ifany exists? Does stress cause poorerpsychological adaptation, or the reverse?Can’t tell with these data. Can proposeyour hypothesis (previous page), but can’tprove this relationship this way.
![Page 4: Longitudinal data](https://reader036.fdocuments.in/reader036/viewer/2022081501/568147f5550346895db52af6/html5/thumbnails/4.jpg)
How about this?
StressPsycho.
adaptation-.36*
Time1 Time2
R2=.20
![Page 5: Longitudinal data](https://reader036.fdocuments.in/reader036/viewer/2022081501/568147f5550346895db52af6/html5/thumbnails/5.jpg)
Well, there are a lot of variables that might be affecting this relationship
Psycho.adaptation
Psycho.adaptation
Time1 Time2
SES
Stress
![Page 6: Longitudinal data](https://reader036.fdocuments.in/reader036/viewer/2022081501/568147f5550346895db52af6/html5/thumbnails/6.jpg)
The recommended method(Pedhazur, 1997): Residualized regression
Psycho.adaptation
Time1 Time2
SES
Stress
Psycho.adaptation
Enteredfirst
All othervariablesenteredsubse-quently Note. However, exogenous variables
like SES, gender, etc. may be entered first as covariates.
R2=.85
R2ch=.02
R2ch=.05
![Page 7: Longitudinal data](https://reader036.fdocuments.in/reader036/viewer/2022081501/568147f5550346895db52af6/html5/thumbnails/7.jpg)
So, how would it work with the stress and coping paradigm?
Stress
Psycho.adaptation
Stress
Psycho.adaptation
Time 1 Time2
![Page 8: Longitudinal data](https://reader036.fdocuments.in/reader036/viewer/2022081501/568147f5550346895db52af6/html5/thumbnails/8.jpg)
How do we assess causality here?
Stress
Psycho.adaptation
Stress
Psycho.adaptation
Time 1 Time2
Stability & autocorrelation
Stability & autocorrelation
A B
A: Stress1 -> Outcome2 B: Outcome1 -> Stress2
![Page 9: Longitudinal data](https://reader036.fdocuments.in/reader036/viewer/2022081501/568147f5550346895db52af6/html5/thumbnails/9.jpg)
A simpler example: Stability and autocorrelation
• Used a dataset by Wheaton et al. (1977), in which they were interested in whether alienation was reasonably stable over a period of 4 years
• Latent variable of alienation, made up of anomie and powerlessness
• Also curious whether socio-economic status would impact on this stability
![Page 10: Longitudinal data](https://reader036.fdocuments.in/reader036/viewer/2022081501/568147f5550346895db52af6/html5/thumbnails/10.jpg)
Wheaton et al. model
Anomie 67 Powerl 67 Anomie 71 Powerl 71
Alienation 67 Alienation 71
1 1
![Page 11: Longitudinal data](https://reader036.fdocuments.in/reader036/viewer/2022081501/568147f5550346895db52af6/html5/thumbnails/11.jpg)
Syntax, of courseStability of alienation, First Model: uncorrelated error terms
DA NI=6 NO=932 MA=KM
KM
11.834
6.947 9.364
6.819 5.091 12.532
4.783 5.028 7.495 9.986
-3.839 -3.889 -3.841 -3.625 9.610
-2.190 -1.883 -2.175 -1.878 3.552 4.503
la
anomia67 power67 anomia71 power71 educatin socioind
se
1 2 3 4 /
MO NY=4 NE=2 BE=SD PS=DI TE=SY
le
alien67 alien71
FR LY 2 1 LY 4 2
VA 1.0 LY 1 1 LY 3 2
PD
OU SE TV MI ND=2
![Page 12: Longitudinal data](https://reader036.fdocuments.in/reader036/viewer/2022081501/568147f5550346895db52af6/html5/thumbnails/12.jpg)
Anomie 67
Powerl 67
Anomie 71
Powerl 71
.31
.37
.27
.39
Alienation 67
Alienation 71
1.0
.95
1.0
.91
.69
.33.77
First model: uncorrelated error terms
R2=.56
![Page 13: Longitudinal data](https://reader036.fdocuments.in/reader036/viewer/2022081501/568147f5550346895db52af6/html5/thumbnails/13.jpg)
How does it fit?
•X2(1) = 61.11
•RMSEA = .25
•NFI = .96
•PNFI = .16
•CFI = .96
•RFI = .81
•Crit. N = 102.09
•GFI = .97
•AGFI = .69
•PGFI = .10
![Page 14: Longitudinal data](https://reader036.fdocuments.in/reader036/viewer/2022081501/568147f5550346895db52af6/html5/thumbnails/14.jpg)
What’s da problem?
• Would like to allow correlated error . . .• But there’s another problem: namely, there’s only 1
df; can’t allow program to estimate any more parameters.
• Ooops, now what? Well, can increase the scope of the model to include other variables, and “borrow” some dfs from those relationships
• Two SES variables: education and socioeconomic indicator
• Make the model a bit more complex (see next page)
![Page 15: Longitudinal data](https://reader036.fdocuments.in/reader036/viewer/2022081501/568147f5550346895db52af6/html5/thumbnails/15.jpg)
Anomie 67 Powerl 67 Anomie 71 Powerl 71
Alienation 67 Alienation 71
1 1
SES 67Education
1
Socio-econindicator
Second model: new latent variable, uncorrelatederror terms
![Page 16: Longitudinal data](https://reader036.fdocuments.in/reader036/viewer/2022081501/568147f5550346895db52af6/html5/thumbnails/16.jpg)
Anomie 67
Powerl 67
Anomie 71
Powerl 71
.34
.34
.30
.36
Alienation 67
Alienation 71
1.0
1.0
1.0
.95
.45
.30.68**
Second model: uncorrelated error terms
SES
Education 67
SEI 67
.31
.58
1.0
.78
-.55*
-.15*
R2=.32
R2=.58
![Page 17: Longitudinal data](https://reader036.fdocuments.in/reader036/viewer/2022081501/568147f5550346895db52af6/html5/thumbnails/17.jpg)
A better fit?
•X2(6) = 71.47
•RMSEA = .11
•NFI = .97
•PNFI = .39
•CFI = .97
•RFI = .92
•Crit. N = 219.99
•GFI = .98
•AGFI = .91
•PGFI = .28
Now, what about correlated error?Would that help?
![Page 18: Longitudinal data](https://reader036.fdocuments.in/reader036/viewer/2022081501/568147f5550346895db52af6/html5/thumbnails/18.jpg)
Anomie 67 Powerl 67 Anomie 71 Powerl 71
Alienation 67 Alienation 71
1 1
SES 67Education
1
Socio-econindicator
Third model: 3 latents & correlated error for anomie
![Page 19: Longitudinal data](https://reader036.fdocuments.in/reader036/viewer/2022081501/568147f5550346895db52af6/html5/thumbnails/19.jpg)
Now, do we have a better fit?
•X2(5) = 6.33
•RMSEA = .02
•NFI = 1.00
•PNFI = .33
•CFI = 1.00
•RFI = .99
•Crit. N = 2218.49
•GFI = 1.00
•AGFI = .99
•PGFI = .24
![Page 20: Longitudinal data](https://reader036.fdocuments.in/reader036/viewer/2022081501/568147f5550346895db52af6/html5/thumbnails/20.jpg)
What about correlated error for powerlessness?
• I ran a fourth model, and the change in chi-square was trivial, in other words, correlated anomie was important, but correlated powerlessness was not.
• Why not? Who knows? Sometimes the same measure carries forward more error than other measures.
• Defensible to correlate all identical measures, but maybe should check to find out whether it makes a difference or not.
![Page 21: Longitudinal data](https://reader036.fdocuments.in/reader036/viewer/2022081501/568147f5550346895db52af6/html5/thumbnails/21.jpg)
Other techniques?
• There are a number of other approaches to longitudinal data.
• Let’s briefly consider the SIMPLEX model• One obtains measures from the same subjects on
the same measure over time, usually more than three times.
• Find that correlations between close time points are higher than between distant time points
![Page 22: Longitudinal data](https://reader036.fdocuments.in/reader036/viewer/2022081501/568147f5550346895db52af6/html5/thumbnails/22.jpg)
Simplex for college grades
• Humphreys (1968) got eight semesters of grade point average (0 to 4 scale)
• Wanted to see how stable the grades were over time
• Simply a matter of computing betas between etas (see next page)
![Page 23: Longitudinal data](https://reader036.fdocuments.in/reader036/viewer/2022081501/568147f5550346895db52af6/html5/thumbnails/23.jpg)
y1 y2 y3 y4
Etc.
A simplex model
![Page 24: Longitudinal data](https://reader036.fdocuments.in/reader036/viewer/2022081501/568147f5550346895db52af6/html5/thumbnails/24.jpg)
Findings
• Findings were not all that earth-shattering:– Correlation between contiguous GPAs were about .90;
between T1 and T8 was .62
– Found that the stabilities (i.e., betas) stayed about the same across time
– Reliabilities of GPA grew slightly over time, in other words, it became a more stable indicator
– Doesn’t tell us anything about the direction of change in the variable (i.e., do GPAs go up, down, or stay the same?). Next method can tell us something about this.
![Page 25: Longitudinal data](https://reader036.fdocuments.in/reader036/viewer/2022081501/568147f5550346895db52af6/html5/thumbnails/25.jpg)
Other methods for analyzing change
• Hierarchical linear modeling (Raudenbush & Bryk) or latent growth curve modeling is all the rage right now.
• Can use LISREL (HLM is sold by SSI too) to perform this analysis. Multilevel modeling (in SAS) does the same thing
• Must have three time points (they don’t have to be equidistant)
• Don’t need a gazillion subjects to do this analysis: big advantage
![Page 26: Longitudinal data](https://reader036.fdocuments.in/reader036/viewer/2022081501/568147f5550346895db52af6/html5/thumbnails/26.jpg)
What’s the logic of HLM?
• Think of it within a regression perspective
• Want to perform a regression in a case where subjects are nested within another variable. For example, students are nested within schools. You have information about school-level variables, but can’t regress these variables in the typical fashion.
![Page 27: Longitudinal data](https://reader036.fdocuments.in/reader036/viewer/2022081501/568147f5550346895db52af6/html5/thumbnails/27.jpg)
Student-level variables: academic ability scores, gender, and socio-economic status
School-level variables: teacher/student ratio,tax dollars spent per pupil, amount of teachertraining.
Dependent variable: grade point average
GPA = slope(ability) + slope(gender) + slope(ratio) + slope(tax)
![Page 28: Longitudinal data](https://reader036.fdocuments.in/reader036/viewer/2022081501/568147f5550346895db52af6/html5/thumbnails/28.jpg)
Individual students
123 students250
students
34students
194students 62
students
Problem: students are nested within a higher level
![Page 29: Longitudinal data](https://reader036.fdocuments.in/reader036/viewer/2022081501/568147f5550346895db52af6/html5/thumbnails/29.jpg)
Why is this a problem?• If you just throw all the variables into a single
regression equation, you would have many students with the same school-level variables.
• You would treat the school-level variables as though they are individual-level variables, i.e., varying for each individual.
• In other words, those values would be correlated among individuals.
• HLM “separates” out the two levels (hence the name, multilevel modeling) in a more appropriate statistical fashion.
![Page 30: Longitudinal data](https://reader036.fdocuments.in/reader036/viewer/2022081501/568147f5550346895db52af6/html5/thumbnails/30.jpg)
Why am I telling you all this?
• You might have an occasion when your data is nested--within institutions, within geographical locations, etc.—and you want to consider both individual-level and group-level data.
• A second reason: it works brilliantly for longitudinal designs in that subjects are nested within age. There are certain statistical advantages in treating the data in this fashion.
![Page 31: Longitudinal data](https://reader036.fdocuments.in/reader036/viewer/2022081501/568147f5550346895db52af6/html5/thumbnails/31.jpg)
0
20
40
60
80
100
120
140
160
1993 1995 1997
Chin-AmerEuro-Amer
Found an Ethnic group X Time of measurementinteraction (p < .001) on PPVT scores
![Page 32: Longitudinal data](https://reader036.fdocuments.in/reader036/viewer/2022081501/568147f5550346895db52af6/html5/thumbnails/32.jpg)
Advantages
• Can learn similar things from repeated measures MANOVA and regression, but HLM is more powerful in its ability to combine variables across nested variables.
![Page 33: Longitudinal data](https://reader036.fdocuments.in/reader036/viewer/2022081501/568147f5550346895db52af6/html5/thumbnails/33.jpg)
Another topic: MIMIC(Multiple indicators and multiple causes)
• Back to LISREL• Sometimes you’ll have exogenous variables
that predict something, and indicators that can be combined into a latent variable, but how does one combine them in a sensible model?
• The exogenous variables are X indicators, and the other variables are Y indicators.
![Page 34: Longitudinal data](https://reader036.fdocuments.in/reader036/viewer/2022081501/568147f5550346895db52af6/html5/thumbnails/34.jpg)
Income
Occu-pation
Educa-tion
Socialparticipation
Churchattend.
Mem-ber-ships
friendsseen
One latent variable is predicted by Xs: mixed model
![Page 35: Longitudinal data](https://reader036.fdocuments.in/reader036/viewer/2022081501/568147f5550346895db52af6/html5/thumbnails/35.jpg)
Mixed models
• The implication is that you can combine observed and latent variables in a single model.
• Why? Might not have multiple indicators of a construct. (But there are ways around this: splitting a measure into 2 or 3 equal parts.)
• Why couldn’t Hodge and Treiman (1968) create a latent variable—SES—from the three X indicators? (see next page)
• May want to know the strength of each specific predictor.
![Page 36: Longitudinal data](https://reader036.fdocuments.in/reader036/viewer/2022081501/568147f5550346895db52af6/html5/thumbnails/36.jpg)
Income
Occu-pation
Educa-tion
Socialparticipation
Churchattend.
Mem-ber-ships
friendsseen
SES
Two latent variables instead of one
![Page 37: Longitudinal data](https://reader036.fdocuments.in/reader036/viewer/2022081501/568147f5550346895db52af6/html5/thumbnails/37.jpg)
The end, or is it just the beginning?
• Thanks for listening, and struggling through a lot of arcane jargon and arbitrary nomenclature.
• I hope that you have a new appreciation for the possibilities of structural equation modeling, whether you use LISREL, AMOS, or EQS.
• May the thought of these possibilities lead you to construct more sophisticated studies and become rich and famous! Well, maybe famous. Okay, maybe mildly known among a few other isolated academics. . . At the least, have fun.