Analysis Consequences of Dependent Measurement Problems in Research on Older Couples

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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). newsomj_at_pdx.edu 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.
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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

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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 wifes sleep may be a
  function of snoring rather than depression

Wifes Depression
Husbands Depression
sleep
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

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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
c
X1
X2
X3
X4
X5
X6
d
f
e
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Effect of Measurement Errors

• The correlation between latent variables is a
  function of several factors

b
Eta 1
Eta 2
a
c
X1
X2
X3
X4
X5
X6
d
f
e
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Effect of Measurement Errors

• Prediction of a dependent variable will be
  underestimated as a result of the overestimation
  of the correlation between exogenous variables

h
Eta 1
Eta 3
j
Eta 2

• Total variance accounted for in dependent
  variable (R2) will be underestimated

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Artificial Data Example Data and Analysis

• Structural equation models using Mplus, version
  2.02 (Muthen Muthen, 1998)
• Artificial correlation matrix as input, N200,
  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

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Artificial Data Example Structural Model
X1
X2
Eta 1
X3
X4
Y
X5
X6
Eta 2
X7
X8
9
Low Correlation Between Latent Variables Smaller
Measurement Error Correlation
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Low Correlation Between Latent Variables Smaller
Measurement Error Correlation
Larger Measurement Error Correlation
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High Correlation Between Latent Variables Smaller
Measurement Error Correlation
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High Correlation Between Latent Variables Smaller
Measurement Error Correlation
Larger Measurement Error Correlation
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Caregiving Example Study Description

• 118 married couples (N108 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 recipients 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

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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

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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 (male0, female1), education, age
• Difficulty rating of 21 ADL/IADLs, 4-point
  scale
• Self-rated health, poor, fair, good, very good,
  excellent

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Caregiving Example Structural Model
not close
too involv- ed
CG conflict
wrong way
Negative Helping Behaviors
dont believe
not close
too involv- ed
resents helping
not courteous
acts angry
critical
CR Conflict
wrong way
dont believe
Gender, Education, Age, ADL/IADLs, self-rated
health
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Relative Effects of Reports of Marital Conflict
on Negative Helping Behaviors
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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

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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.