Title: Using%20repeated%20measures%20data%20to%20analyse%20reciprocal%20effects:%20the%20case%20of%20Economic%20Perceptions%20and%20Economic%20Values
1Using repeated measures data to analyse
reciprocal effects the case of Economic
Perceptions and Economic Values
- Patrick Sturgis,
- Department of Sociology, University of Surrey
- Peter Smith, Ann Berrington, Yongjian Hu,
Department of Social Statistics, University of
Southampton
2Reciprocal Causality
- Often viewed as a nuisance to be removed
(simultaneity bias). - But can be of substantive and policy interest.
- Achievement/self-esteem
- Anti-social behaviour/depression
- Problematic to estimate with observational data.
3Overview
- Approaches to estimating reciprocal effects.
- General Linear Model
- Instrumental variable approaches
- Cross-lagged panel models
- Errors of Measurement
- Unobserved variables and error covariance
- Example economic values and perceptions
- Conclusions
4True Model
a
X
Y
b
5Standard Approach X-Sectional Data
(Ignore the problem)
c
Y
X
Y
X
c f(a b)
6Instrumental Variables Approach
Instruments
Instruments
X
Y
7cross-lagged panel model
- cross-lagged panel model (Campbell 1960 Campbell
and Kenny 1999 Finkel 1995 Marsh and Yeung
1997). - Particularly useful for examining questions of
reciprocal causality. - Each Y variable is regressed onto its lagged
measure and the lagged measure of the other Y
variable(s) of interest. - Can the history of X predict Y, net of the
history of Y (Granger causality)? - Problematic for correlational designs (Rogossa
1995). - But with SEM it is much more powerful (Marsh
1993 1997).
8Cross-lagged Panel Model
Yt1
Yt0
Xt1
Xt0
9Problems with this model
- 2 waves limited information about causal
relationship. - Concepts are assumed to be measured with zero
error. - No account taken of correlations between
disturbances of endogenous variables.
10Consequences of Measurement Error
- All measurements of abstract concepts will
contain error. - Error can be stochastic ( ) or systematic
- ( ) .
- Systematic error biases descriptive and causal
inferences. - Stochastic error in dependents leaves estimates
unbiased but less efficient. - Stochastic error in independents attenuates
effect sizes. - Both problematic for hypothesis testing and
causal inference.
11Correction for Measurement Error
Specify each concept of interest as a latent
variable with multiple indicators
Specify error covariance structure
d1
12Correlated Disturbances 1
- The disturbance terms for the same endogenous
variable over time are likely to be correlated. - Similarly, the disturbance term for the 2
endogenous variables are likely to be correlated
at the same time point. - Caused by unobserved variable bias a third
variable, Z, may be causing both Y variables
simultaneously. - Failing to consider these parameters can bias
stability and cross-lagged estimates (Williams
Posakoff 1989 Anderson Williams 1992).
13Correlated Disturbances 2
14Example Economic Perceptions Values
- Left-right economic value posited as fundamental
explanatory variable for political preferences
vote (Feldman 1989 Bartle 2000). - Similarly, perceptions of economic performance
are seen as crucial determinants of electoral
outcomes (Lewis-Beck Stagmaier 2000). - What is the relationship between them?
- Different macro-economic conditions require
different approaches to economic policy. - Peoples left-right leanings are likely to
influence their perceptions of economic
performance (Evans and Andersen 1997).
15Data and Measures
- Data come from the 1992-1997 British Election
Panel Study. - Analytical sample those interviews at all five
waves (n1640). - Left-right value measured by 6 item scale (Heath
et al 1993). - Economic perceptions measured by 3 items tapping
retrospective (past year) perceptions of - Level of unemployment
- Rate of inflation
- Standard of living
16Cross-sectional Model
17IV Model
.17
-.31
.12
.67
.50
18Cross-lagged Observed Score Model
.04
.26
.26
.68
19Cross-lagged latent 2 wave
1.01
.97
.53
.48
.12
-.10
.58
.27
20Cross-lagged latent 5 wave
a
a
c
c
etc.
d
d
b
b
21Cross-lagged latent Pooled Effect(zero
disturbance covariances)
Chi Square 2671 df1024 plt0.001 IFI .938
RMSEA .031
22Cross-lagged latent 5 wave(correlated
disturbances)
23Cross-lagged latent Pooled Effect(disturbance
covariances estimated)
Chi Square 2537 df1050 plt0.001 IFI .943
RMSEA .029
24Summary of Cross Lagged Effect Estimates
25Conclusions
- Reciprocal relationships can be seen as either a
nuisance or of substantive interest. - Either way, they are hard to model with
observational data. - Repeated measures data offers significant
leverage relative to x-sectional. - Problems of error variance and covariance much
greater with panel data. - Need to correct for errors in the measurement of
abstract concepts. - And estimate relationships between measurement
errors over time.
26Conclusions
- Unobserved variable bias likely to manifest
through covariance between residuals. - Failure to model these errors and their
covariance structures can lead to seriously
biased causal inference. - Naïve analyses showed strong non-recursive
relationship between economic values and
perceptions. - More appropriate treatment of error structures
altered causal inference substantially.