Discrete choice analysis

A DCE has a number of uses. It may be used to explore strengths of preferences, trade-

offs, and MRS. There are various discrete choice models that can be employed to

analyse preferences, as described in Chapter 2 (section 2.5.2.5). The DCE undertaken

in this study has a number of objectives, as outlined below.

4.2.2.1 Search for best specification of preferences on the unforced choice

Different discrete choice models are employed to analyse women’s preferences for

maternity care. A standard conditional logit (CL) model is used initially to analyse

preferences. The individual choice probability for the CL model is given by the logit

specification, described in Chapter 2 (Eqn. 2.10). The CL model is used as a

‘benchmark’ model to investigate how preferences change given changes in assumptions about respondents’ choices. In the first instance, two separate CL models are estimated to identify the best specification of the quantitative attributes (cost and

length of stay). These models test the linearity of the quantitative variables by first

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estimated where the attributes are treated qualitatively (effects coded). Ensuring that

the cost attribute is linear is important for subsequent willingness to pay estimations.

The CL model is then compared with more flexible models to assess assumptions about women’s preferences. An important limitation of the CL model lies in the property of independence of irrelevant alternatives (IIA), which assumes perfect

substitutability across alternatives. Since certain alternatives within a choice set may

be closely correlated with each other, the assumption that the choice probabilities are

proportionately affected when a new alternative is introduced may be unrealistic. This

assumption may be relaxed by using the nested logit (NL) model where IIA must hold

within nests, but not across them. The NL model generates a dissimilarity parameter (λ), or inclusive value, that describes the degree of independence between each alternative within a nest. In order for the NL model to be consistent with random utility theory the dissimilarity parameter must lie between 0 < 𝜆 ≤ 1 (McFadden 1978). The choice probability is given by:

𝑃_{𝑖(𝑔)𝑛} = 𝑃 (𝑛𝑒𝑠𝑡 𝑔) ∙ 𝑃(𝑖, given nest 𝑔) (4.1)

where the probability of choosing alternative 𝑖 from nest 𝑔 for individual 𝑛 is dependent on the probability of 𝑖 coming from nest 𝑔. This two stage decision process includes two levels of analyses within the NL model. At the higher level, certain

factors (or demographics) are assumed to influence which nest an individual chooses,

while at the bottom level, the same attributes underline the utility function for each

nest (Amaya-Amaya et al 2008).

The NL model is especially attractive given the inclusion of an opt-out option which

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that respondents adopt a two-stage decision-making process by first deciding whether

or not they want to consume a maternity care alternative (A/B versus Neither), and

then which maternity care alternative they would prefer (A versus B). Therefore, the

two experimental alternatives and the opt-out option would belong to two different

nests where the property of IIA must only hold within the nests. The CL model with

an alternative specific constant (ASC) for the opt-out option is compared with the NL

model to identify which model best accounts for the unobserved data-generation

process (Haaijer et al 2001).

4.2.2.2 Analysis of the dual response choice (DRC) format

The dual response choice (DRC) format has two functions. First, the DRC is used to

identify which discrete choice data should be used for the estimation of women’s preferences (i.e. unforced choice scenario, forced choice scenario, or a merged dataset

of both). A CL model is used on the unforced and forced choice scenarios separately.

The unforced choice scenario is then reduced to a pairwise (or forced) choice scenario

where the opt-out option is excluded. This pairwise dataset is merged with data from

the forced choice scenario and estimated using a CL model, similar to other analyses

(Brazell et al 2006; Collins and Rose 2013; Pedersen et al 2012).

These models are compared with the ‘benchmark’ model to identify the discrete choice data that should be used for further analysis. The models are compared in terms of

“information”. Since discrete choice data are based on the log likelihood function, information criteria are available on Akaike’s information criteria (AIC) and Bayesian information criteria (BIC) (StataCorps 2011a).

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𝐵𝐼𝐶 = −2𝑙𝑛𝐿 + 𝑘𝑙𝑛𝑁 (4.3)

where 𝑙𝑛𝐿 is the maximised log-likelihood, 𝑘 is the number of parameters being estimated, and 𝑁 is the sample size. In both cases, the best fitting model is the one with the lower AIC and BIC values (StataCorps 2011a).

The second function of the DRC is to examine choice consistency. Since the DRC is

a relatively new development in the DCE literature, there is a paucity of research

examining the effect of this approach on choices. This analysis contributes to the

growing body of work on the DRC format by examining choice consistency across the

unforced and forced choice scenarios (Brazell et al 2006; Collins and Rose 2013;

Giergiczny et al 2013; Pedersen et al 2012). It is likely that choices made in the forced

choice scenario differ to choices made in the unforced choice scenario as motivations

and interest wane after the initial task (Giergiczny et al 2013; Collins and Rose 2013).

To allow for scale differences in parameters arising from the two different datasets

(unforced and forced choice), a heteroscedastic CL model is estimated, similar to other

analyses (Collins and Rose 2013; Pedersen et al 2012). This heteroscedastic CL model

tests the consistency of choices across the two choice scenarios.

4.2.2.3 Exploring preferences using a flexible discrete choice model

Another limitation of the CL model relates to random taste variation. The standard CL

model estimates fixed effects only, and assumes that elicited preferences are

representative of the entire sample (Amaya-Amaya et al 2008). However, it is unlikely

that individuals derive the same utility from each of the attributes on offer.

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random parameters or mixed logit (MXL) model (Eqn. 4.4). For any individual the

choice probability is:

𝑃_𝑛𝑖 (𝜃) = ∫ 𝐿_𝑛𝑖(𝛽)𝑓(𝛽|𝜃)𝑑𝛽 (4.4)

where n are random variables and θ are the parameters of the distribution. The MXL

model generates mean utility estimates for each attribute, and standard deviations of

the random coefficients to reflect heterogeneity among individuals in the sample.

Using the appropriate dataset, a number of MXL models are estimated to identify the

best specification of women’s preferences. In the first instance, the MXL model is specified with one random attribute. This is increased in subsequent models until the model which best describes women’s preferences is estimated. Different specifications of the cost attribute are also assumed (i.e. normal versus lognormal distribution).

MRS are calculated for each of the attributes against the cost attribute (Ryan et al

2008b) (Eqn. 4.5). This generates information on women’s marginal willingness to

pay for a specified level of an attribute in the DCE. The WTP calculations are

performed in Stata v.12 using the Delta method (Hole 2007; StataCorps 2011a).

𝑊𝑇𝑃 = 𝛽_𝐾/−𝛽_{𝑝𝑟𝑖𝑐𝑒𝑝𝑟𝑜𝑥𝑦} (4.5) Two factors are assumed to influence women’s preferences: previous obstetric

experience and geographic location. The literature suggests that experience plays a

considerable role in influencing preferences (Ryan and Ubach 2003), particularly

within maternity care where women are more likely to choose a service if they have

experienced it (Cartwright 1979). This analysis investigates this finding in an Irish

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or knowledge of a service’s availability (Ryan and Ubach 2003; Salkeld et al 2000). The two maternity units present an interesting opportunity to assess whether

preferences differ across two geographic locations where the type of service provided

in each region differs. In CUMH, the only model of care on offer is consultant-led

care. In the NMH, a hybrid model of care, which encompasses features of both

consultant- and midwifery-led care is provided. This analysis investigates whether

preferences are driven by the type of service provided in each region; that is, are

women from CUMH likely to prefer consultant-led care than women from the NMH

who may have stronger disposition towards midwifery-led care. To investigate

whether these factors influence preferences, a series of subgroup analyses are

performed, with MRS calculated for each model.

This section (4.2.2) focussed on the estimation of preferences using discrete choice

analysis. Several objectives are contained in this analysis, as outlined above, and

certain factors that are assumed to influence preferences are tested in an Irish context.

The DCE has several other objectives relating to welfare measures and policy analysis.

These objectives are the focus of section 4.2.3.