The structural equations

5.3

5.3

5.3

The structural equationsThe structural equations The structural equationsThe structural equations

Structural parameters of the health and engagement equations (4) and (6) are

provided in Table 4. The latent poor-health index (ℎ∗) is higher for non-white women and is non-linearly associated with age of the respondent.22 _SES-related

differences in health are clearly evident by looking at the magnitude and signifi-

cance of the coefficients associated with educational attainments, social class and

home-ownership. Highly educated individuals have significantly better average

health than otherwise similar less educated people. Similarly, high social class

and housing wealth are also associated with better health.

T TT

TABLE ABLE ABLE ABLE 4:4:4:4:Structural parameters of the health (ℎ∗) and engagement (𝑒∗) equa-

tions

Covariate ℎ

∗ _𝑒∗

Coefficient S.E Coefficient S.E

Female 0.050** 0.024 -0.260*** 0.045

Spline age 65-74 -0.006* 0.001 -0.016 0.011

Spline from age 74+ a _{0.017*** 0.003 -0.042*** 0.008}

Married/cohabiting 0.032 0.028 0.149** 0.066

Completed education before 14 years old 0.186*** 0.028 -0.055 0.066 Completed education after 19 years old -0.245*** 0.051 -0.172 0.117

Non-white 0.543*** 0.083 -0.865*** 0.154

Home-owner -0.302*** 0.031 0.137* 0.072

Social class: manual worker 0.177*** 0.027 -0.187*** 0.061

Notes: * p < 0.05, ** p < 0.01, *** p < 0.001. (a_{) collapsed at 90. Estimates in the table refers}

to model D specification (see later in the text). The model also includes dummy variables on region of residence, if living in urban area (>10K), and from which HSE cross-section the eligible person was drawn. Standard errors were clustered at household level.

22 _{Sample members’ age enters in all structural equations in the form of a spline with a knot at the}

median age (74). It accounts for possible non-linearities in its relation with health (equation (4)), engagement (equation (6)) and retention to the study (equation (2)).

46

Engagement with the scope of the survey (𝑒∗) is lower for older non-white women and higher for partnered individuals. One might expect a SES-engage-

ment gradient, in line with the idea that high SES individuals are more likely to

perceive the social benefits of complying with the scope of the survey (Uhrig,

2008), but our results are not consistent with that. Home-owners show a higher

level of engagement (significant at 10% level) and low social class is negatively

associated with engagement (p-value <0.001) but, surprisingly, we do not find

any significant association of 𝒆∗ with level of education. This result is consistent with findings in Jenkins

et al.

(2006) where education was not significantly asso-

47 T

T T

TABLE ABLE ABLE ABLE 5:5:5:5:Estimates of retention in the survey in wave 1 of ELSA

Covariate Model A Model B Model C Model D

Coefficient S.E Coefficient S.E Coefficient S.E Coefficient S.E

Female -0.107*** 0.023 -0.111*** 0.023 0.001 0.032 -0.002 0.032

Spline age 65-74 0.001 0.007 0.001 0.007 0.011 0.009 0.010 0.008

Spline from age 74+ a _{-0.027*** 0.004 -0.027*** 0.004 -0.012** 0.006 -0.012** 0.006}

Married/cohabiting -0.079** 0.036 -0.081** 0.036 -0.175*** 0.048 -0.177*** 0.048

Completed education before 14 years old -0.096*** 0.036 -0.095*** 0.036 -0.099** 0.048 -0.097** 0.048

Completed education after 19 years old 0.082 0.064 0.087 0.065 0.208** 0.082 0.211** 0.082

Non-white -0.230** 0.102 -0.226** 0.102 0.155 0.137 0.157 0.137

Home-owner -0.001 0.041 -0.003 0.041 -0.061 0.052 -0.063 0.052

Social class: manual worker -0.104*** 0.033 -0.104*** 0.033 -0.039 0.044 -0.040 0.044

ℎ∗ _{-0.042*** 0.016 -0.047*** 0.016 -0.016 0.021 -0.023 0.021} (ℎ∗₎2 _{-0.030** 0.013 -0.026* 0.015} 𝑒∗ _{0.521*** 0.030 0.520*** 0.03} 𝑐𝑜𝑣(ℎ∗_{, 𝑒}∗_{) -0.072** 0.030 -0.073** 0.03} Free parameters 45 46 55 56 Log-likelihood -49783.925 -40620.272 -49434.928 -49433.378

Correction for non-normality factor 1.1286 1.548 1.1333 1.1321

AIC 99769.85 81452.544 99075.856 99074.756

BIC 100480.725 82198.611 99800.808 99806.746

Notes: * p < 0.05, ** p < 0.01, *** p < 0.001. (a_{) collapsed at 90. All models also include dummy variables on region of residence, if living in urban area}

48

Structural parameters of the retention model (equation (2)) are provided in

Table 5 in four different variants.

Model A

is a reduced version in which latent

health enters linearly and we do not control for latent engagement.

Model B

introduces a quadratic term for health aiming at testing its possible non-linear

relationship with retention in wave 1.

Models C

and

D

introduce latent engage-

ment in the set of covariates when ℎ∗ is entered linearly and in a quadratic form. For model A, we found results in line with previous research. Older married

women are less likely to remain in the study as well as the non-white population.

Lower education and social class are negatively associated with participation in

wave 1 of ELSA but we did not find any significant relationship with home own-

ership.

In model A, there is a positive relationship between health and survey partici-

pation: poor-health significantly reduces the likelihood of retention in wave 1 but

model B, which fits the data slightly better than model A, reveals a significant

U-shape relationship, meaning that, while unhealthy individuals are less likely to

remain in the study at follow-up, very healthy individuals do not show signifi-

cantly lower dropout probabilities with respect to the remaining sample popula-

tion. This is consistent with the view that healthy people might have concerns

about the time cost of participating and in taking part in medical and cognitive

tests which, apart from being time-consuming, may also be felt to be humiliating.

49

for retention when latent health enters in the model linearly and in a quadratic

form, respectively. Both specifications show that the latent engagement index

plays the most important role in explaining retention decision for wave 1, by

increasing the explained variance significantly, as shown from the goodness of fit

statistics available at the bottom of Table 5.

Controlling for engagement, the effect of other covariates is significantly weak-

ened. Gender, race, home-ownership and social class no longer play a significant

effect in explaining retention in the study. The coefficient associated with the

second spline of age23 _{is almost halved, whereas the effect of being partnered is}

now about 2.2 times higher those obtained in models A and B. Similarly, the

effect of level of education is significantly increased, with an emerging significant

retention bias in favour of those more educated.

Controlling for engagement, latent health is no longer significantly related to

wave 1 participation when its effect is assumed to be linear (model C). The coef-

ficient of the quadratic term of ℎ∗ in model D is now significant only at the 10% level. Both specifications provide evidence that, controlling for the individual’s

engagement at baseline, health plays a minor role in explaining participation in

wave 1.

There is a small but significant correlation between ℎ∗ and 𝑒∗ of about -0.07,

23 _{See previous footnote for a definition.}

50

p<0.05, consistent with the idea that people in poor health face higher costs in

retrieving all the information required in formulating a response or are more

sensitive to privacy concerns (Beatty & Herrmann, 2002; Dunn

et al.

, 2004; Jen-

kins

et al.

, 2006; Kho

et al.

, 2009) and are less engaged. This has to be taken into

account when drawing conclusions from estimates in Table 5. A series of robust-

ness checks are confined in the Appendix. For example, constraining the correla-

tion between the two latent constructs to zero increases the importance of ℎ∗ in explaining retention in wave 1 but leaves other structural coefficients virtually

unaffected (see Appendix Table A1).

In document Latent factor modelling of disability (Page 55-60)