Page 58 - IJPS-3-1

Disability policies and public views on work disability...
Pr h i s  k  Pr  k l  x i   

 k
h
 x
s
k
l


 Pr
Pr

s
h
where is respondent i’s self-reported severity of work limitation, k is the severity
i
i
i
s
h
level ranging from 1 = none to 5 = extreme, x i is a vector of observed characteristics for
s

i
i
k
respondent i, and is a random error term. µ refers to the cut-point between severity


s
 Pr

l 

h 
Pr
k
k
v
v

l
a 
v
 
i
i
i
v
v
categories on the reporting scale. Pr h i v  k Pr k l   a     i l 
The model estimates the probability of a respondent reporting a given category of
severity for their work limitation along a latent (continuous) index of work limitation
severity that is a function of their individual characteristics. The model also estimates
1
4
the cut-points, µ to µ , as the model parameters, representing the thresholds at which a
respondent would change their work limitation ratings along the latent index.
The model assumes that cut-points are constant across individuals. That is,
the locations of the cut-points are invariant across respondents (i.e., reporting
homogeneity). If this assumption does not hold, in particular, if the cut-points vary
with the respondents’ characteristic x i , then imposing this assumption will lead to
biased estimates of the coefficient β. This is because β will reflect both health effects
(effects of covariate x i on work limitation severity) and reporting effects (effects of
covariate x i on the cut-points).
To test and estimate flexible models that allow the cut-points to vary with
respondents’ characteristics, we will need external information to identify the
parameters in the cut-points equations. Vignette data can be used as such external
information to model the cut-points as functions of respondent characteristics.
Respondents are asked to rate identical vignette characters’ work limitations. The
vignettes are fixed, so the variations in ratings represent differences in response scales
used by respondents.
In a generalized ordered probit model, we estimate respondents’ severity rating of
the vignette character’s work limitation:
v
v
v
Pr (h = ) k = Pr (µ k−1 ≤ a + ε < µ i k )
i
where
k
k
k
k
k
µ = γ + x γ + (2)
z δ +
cη
0
i
i
c
ν
ν
Each vignette, α , is constant, plus a random error, ε . The model estimates the
probability of a respondent reporting a given severity category for the vignette
character’s work limitation, allowing the location of cut-points to vary by respondents’
characteristics. Specifically, the vignette rating is estimated as a function of a vignette
dummy with each cut-point separately estimated as a function of respondents’
characteristics which includes both individual-level factors and country-level factors.
The threshold equation (2) is estimated separately for each of the four cut-points,
1
4
µ to µ , which is determined by respondent i’s characteristic x i , disability policy
generosity of country c in which the respondent resides, z c , and other country-specific
factors summarized in a vector of country indicator, c. Our main interest, the effect
k
of disability generosity, δ , reflects the shift of the cut-point µ as the disability policy
k
generosity score varies. A negative estimate of δ would suggest that respondents under
k
a more generous disability regime apply a lower threshold to classify the disability
severity level k, that is, they are more likely to evaluate a given vignette person as
more severely work limited. The estimated coefficients for the four cut-point equations
are presented in Table 4.
Finally, we impose the cut-points, which are estimated based on respondents’ ratings
of the vignette characters’ work limitations, on the model that estimates respondents’
ratings of their own work limitations (equation (1)). The two models, equations (1)
and (2), are jointly estimated with the Hierarchical Ordered Probit (HOPIT) procedure
suggested by King et al. (2004). The vignette model, equation (2), estimates the four
cut-points as functions of respondents’ characteristics, thus allowing for reporting
heterogeneity. The self-reported work limitation model, equation (1), represents
the relationship between the respondents’ own work limitation severity and their
characteristics, with reporting cut-points determined by the vignette model. The
52 International Journal of Population Studies 2017, Volume 3, Issue 1