Transcript Document

Analysis Consequences of Dependent Measurement
Problems in Research on Older Couples
Jason T. Newsom
Institute on Aging
Portland State University
Presented at the 55th annual meeting of the Gerontological Society of America, Boston,
MA (November, 2002). [email protected]
This research was supported by grant AG5159 from the National Institute on Aging. I
thank Nicole Adams, Azra Rahim, Heather Mowry, Joe Rogers, Phillip King, Thea Lander,
and Reggie Silbert for assistance with data collection.
1
Background
• A common research question involves comparison of the unique effects of a variable
measured for each member of the couple on a dependent variable
• Example: husbands’ and wives’ perceived stress as predictors of life satisfaction
• When identical measures are used for each dyad member, the within-dyad
correlation can be overestimated because of correlated measurement errors
• The overestimation of the within-dyad correlation will lead to an underestimation of
the unique (partial) relationships to a dependent variable
2
Correlated Errors
• A correlated measurement error is an association between two items beyond that due
to the correlation between their respective latent variables
• Example: Husband and wife’s sleep may be a function of snoring rather than
depression
Wife’s
Depression
sleep
Husband’s
Depression
sleep
• Correlated errors can occur with any two latent variables, but they are
especially likely when parallel item sets are used to measure a construct in
two members of a dyad
• May be due to item content, specific wording, or methodological factors
3
Effect of Measurement Errors
• Focus on measurement errors among predictor (exogenous) variables
• If correlated errors exist but are not estimated, the correlation between
the latent variables will be overestimated
b
Eta 1
Eta 2
a
X1
c
X3
X2
f
X4
X5
X6
d
e
4
Effect of Measurement Errors
• The correlation between latent variables is a function of several factors:
r14  abc  e
abc  r14  e
r e
b  14
ac
b
Eta 1
Eta 2
a
X1
c
X3
X2
f
X4
X5
X6
d
e
5
Effect of Measurement Errors
• Prediction of a dependent variable will be underestimated as a result of the
overestimation of the correlation between exogenous variables
Eta 1
h
Eta 3
j
Eta 2
• Total variance accounted for in dependent variable (R2) will be
underestimated
6
Artificial Data Example
Data and Analysis
• Structural equation models using Mplus, version 2.02 (Muthen & Muthen, 1998)
• Artificial correlation matrix as input, N=200, standardized coefficients
• Correlation with dependent variable = .25, varied correlation among items
• Single replication for each variation (i.e., effects of sampling variability were
not examined)
• 2 exogenous latent variables, 4 indicators each
• Single measured dependent variable
• Comparison of parameters with and without correlated errors
7
Artificial Data Example
Structural Model
X1
X2
Eta 1
X3
X4
Y
X5
X6
Eta 2
X7
X8
8
Low Correlation Between Latent Variables
Smaller Measurement Error Correlation
With
Correlated Errors
Without
Correlated Errors
Correlation of exogenous latent
variables
.200*
.250**
 91
Y regressed on Eta1
.295***
.283***
 92
Y regressed on Eta2
.295***
.283***

Correlated measurement error
.100*
fixed at 0
Parameter
 12
Description
ij
9
Low Correlation Between Latent Variables
Smaller Measurement Error Correlation
With
Correlated Errors
Without
Correlated Errors
Correlation of exogenous latent
variables
.200*
.250**
 91
Y regressed on Eta1
.295***
.283***
 92
Y regressed on Eta2
.295***
.283***

Correlated measurement error
.100*
fixed at 0
Parameter
 12
Description
ij
Larger Measurement Error Correlation
With
Correlated Errors
Without
Correlated Errors
Correlation of exogenous latent
variables
.200*
.350***
 91
Y regressed on Eta1
.295***
.262**
 92
Y regressed on Eta2
.295***
.262**

Correlated measurement error
.300***
fixed at 0
Parameter
 12
ij
Description
10
High Correlation Between Latent Variables
Smaller Measurement Error Correlation
With
Correlated Errors
Without
Correlated Errors
Correlation of exogenous latent
variables
.600***
.650***
 91
Y regressed on Eta1
.221*
.214
a
 92
Y regressed on Eta2
.221*
.214
a

Correlated measurement error
.100*
fixed at 0
Parameter
 12
Description
ij
11
High Correlation Between Latent Variables
Smaller Measurement Error Correlation
With
Correlated Errors
Without
Correlated Errors
Correlation of exogenous latent
variables
.600***
.650***
 91
Y regressed on Eta1
.221*
.214
a
 92
Y regressed on Eta2
.221*
.214
a

Correlated measurement error
.100*
fixed at 0
Parameter
 12
Description
ij
Larger Measurement Error Correlation
With
Correlated Errors
Without
Correlated Errors
Correlation of exogenous latent
variables
.600***
.750***
 91
Y regressed on Eta1
.221*
.202
ns
 92
Y regressed on Eta2
.221*
.202
ns

Correlated measurement error
.300***
fixed at 0
Parameter
 12
Description
ij
12
Caregiving Example
Study Description
• 118 married couples (N=108 due to missing data)
• Community sample from Portland, OR metropolitan area
• Caregivers and care recipients interviewed about helping transactions
• Examine relationship between perceptions of marital conflict (as
reported by both caregivers and care recipient) and recipient’s reports of
negative helping behaviors
• Care recipients had difficulty with one or more ADL/IADLs due to
wide range of health conditions (e.g., arthritis, claudication, knee
problems, heart disease)
• Covariates: gender, education, age, ADL/IADL difficulties, self-rated
health
13
Caregiving Example
Measures
• Dependent variable: negative helping behaviors
• “When my spouse has to help me, he/she becomes angry”
• “When I need help with something, my spouse is critical of me”
• “My spouse seems to resent helping me”
• “When my spouse helps me do something, he/she is always courteous”
(reversed)
• 4-point scale of agreement
14
Caregiving Example
Measures
• Independent variables:
• Marital conflict as reported by caregiver and care recipient (Skinner,
Steinhauer, Santa-Barbara, 1983; Williamson & Schulz, 1992).
• 4 items on 5-point scale of agreement (e.g., “My spouse gets too
involved in my affairs”)
• Gender (male=0, female=1), education, age
• Difficulty rating of 21 ADL/IADLs, 4-point scale
• Self-rated health, poor, fair, good, very good, excellent
15
Caregiving Example
Structural Model
not
close
too
involved
wrong
way
CG
conflict
Negative
Helping
Behaviors
don’t
believe
not
close
too
involved
wrong
way
CR
Conflict
acts
angry
critical
resents
helping
not
courteous
don’t
believe
Gender, Education, Age, ADL/IADLs, self-rated health
16
Relative Effects of Reports of Marital Conflict on
Negative Helping Behaviors
Description
With
Correlated Errors
Without
Correlated Errors
Correlation between conflict latent variables
.259
.347*
CG marital conflict  unhelpful behaviors
.391*
.339
CR marital conflict  unhelpful behaviors
.431**
.398**
Gender (0=male, 1=female)
-.242
Education
.147
.131
Age
.109
.126
IADL/ADL difficulties
.046
.049
Self-rated health
-.080
-.113
Correlated measurement error 1 (not close)
.242**
fixed at 0
Correlated measurement error 2 (too involved)
-.029
fixed at 0
Correlated measurement error 3 (wrong way)
.219**
fixed at 0
Correlated measurement error 4 (don’t believe)
-.085
fixed at 0
.430
.392
Total R
2
a
a
-.222
a
p<.10, * p<.05, ** p < .01, *** p< .001
2
Model fit (correlated errors model):  (92) =118.893, p = .03, IFI = .936,
SRMR = .062
17
Summary
• Bias in predictive paths:
• Increases with larger or more measurement error correlations
• Only occurs to the extent that exogenous variables are correlated
• Can have biasing effect on other covariates in the model
• Not limited to dyadic data, but most likely when item wording is strictly
parallel (e.g., friend instrumental support, friend emotional support)
• Modification indices or nested tests can be used, but at least with small
samples a priori estimation is encouraged
• Bias occurs in regression or hierarchical linear models
18
Further Readings
Cook, W.L. (1994). A structural equation model of dyadic relationships with the family
system. Journal of Consulting and Clinical Psychology, 62, 500-509.
Kashy, Deborah A; Kenny, David A. The analysis of data from dyads and groups. In H.T.
Reis & C.M. Judd (2000). Handbook of research methods in social and personality psychology.
(pp. 451-477). New York, NY, US: Cambridge University Press.
Kenny, D. A., & Cook, W. (1999). Partner effects in relationship research: Conceptual
issues, analytic difficulties, and illustrations. Personal Relationships, 6, 433-448.
Newsom, J.T. (2002). A multilevel structural equation model for dyadic data. Structural
Equation Modeling, 9, 431-447.
Gerbing, D. W., & Anderson, J.C. (1984). On the meaning of within-factor correlated
measurement errors. Journal of Consumer Research, 11, 572-580.
Gillespie, M. W., & Fox, J. (1980). Specification errors and negatively correlated
disturbances in "parallel" simultaneous-equation models. Sociological Methods and Research,
8, 273-308.
19