Confidential
THE RELATIVE IMPORTANCE OF PRODUCT AND BRAND
CHARACTERISTICS IN CHOOSING A HEALTH INSURANCE
by
Marieke van Wijhe
University of Groningen
Faculty of Economics and Business
MSc Marketing Intelligence
January, 2018
S2017296
l.m.van.wijhe@student.rug.nl
+31642999170
Supervisors: prof. dr. T.H.A. Bijmolt & dr. F. Eggers
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SUMMARY
In 2006 the health insurance system in The Netherlands was drastically reformed by the introduction of a model with managed competition. This means that health insurers are provided with incentives to act as prudent buyers of care on behalf of their enrollees. Therefore, insurers need to understand consumers’ preferences for health insurances. Although a previous study quantified consumer preferences and trade-offs between these attributes, we identified three reasons why additional research was needed. First, the data of this study was collected at the time of a government’s proposal allowing insurers to set a lower level of reimbursement of care by non-contracted providers. This proposal was heavily disputed by the medical profession and widely covered by the media, which may have biased their results. Second, in the past years, multiple health insurers introduced a health program which should lead to a reduction in healthcare costs and add value to the insurance and the insurer’s brand. Research showed that health apps are a promising future direction for care, but the effect of such programs on consumers’ preferences for an insurer that offers a health program has not been analyzed in previous research. Third, previous studies in the field of health insurance did not account for brand effects. Finally, this study pays more attention to considerations regarding craft to establish higher external validity than in previous studies.
Therefore, we quantified consumers' trade-offs between (basic) health insurance (i.e. product) characteristics while accounting for brand effects by a discrete choice experiment (DCE). The DCE consisted of 15 choice sets, each involving two hypothetical basic health insurances. We selected five health insurance characteristics to be included in the DCE: insurer, Attribute 1, Attribute 2, Attribute 3, and Attribute 4. This selection was based on a literature study including previous stated- and revealed-preference studies on the same topic. Also, it is based on the specifications of basic health insurances that are provided on insurers’ websites and comparison websites, as many consumers use those sources of information to make decisions. In addition, we identified five brand characteristics that could explain and specify an insurer’s brand effect: familiarity, perceived medical selection, perceived profit objective, trustworthiness, and quality of care. We determined which brand perception attributes should be analyzed by examining insurers’ websites to find out which brand characteristics are communicated and thus likely to be perceived by consumers. In addition, we conducted interviews with experts in the field of health insurance. A health insurance company in The Netherlands is used as focus brand in this thesis.
The study is based on a large, representative sample of the national adult population (n=433). This enables us to find out whether the consumer preferences differ according to sociodemographic characteristics.
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model enabled us to calculate the (relative) willingness-to-pay for four insurers and a fake brand. Brand D is the second most valuable brand, after Brand E; consumers are willing to spend €6.29 (of a monthly premium) more for Brand D than for the fake brand GMK. We also performed market simulations, for example to find the absolute willingness-to-pay for the focus offer of Brand D compared to the none option, which is a preference for the status quo, i.e. preference to stay with the current insurer. This simulation showed that Brand D is more preferred than the none option when Brand D’s premium is lower than €98.99. In addition, we estimated a latent class model (LCM) which also included the brand perception attributes and covariates. The model revealed five actionable segments: Brand Lovers, Value-seeking Pragmatists, Satisfied Status quo’ers, Well-covered Passives, and Price-sensitive Switchers. Brand characteristic i1 was by far the most decisive characteristic for the Brand Lovers. Three segments, Value-seeking Pragmatists, Satisfied Status quo’ers, and Price-sensitive Switchers, showed that their current insurance (i.e. none option) and the insurance’s level of Attribute 1 are important choice determinants. Their preferences differ according to sociodemographic characteristics. The most decisive characteristics for the Well-covered Passives are their current insurance (i.e. none option) and the insurance’s level of Attribute 2. In this LCM, the effect of Attribute 3 remained insignificant.
Furthermore, we found two brand characteristics that can explain and specify the brand effect: Brand characteristic i1 and Brand characteristic i3. These attributes cause insignificant brand residuals.
Obviously, the relative importances of these attributes differ across segments.
3 CONTENTS Summary 1 1. Introduction 6 1.1 Study background 6 1.2 Research gap 6 1.3 Brand effects 7 1.3.1 Brand information 7
1.3.2 Information in health insurance choice process 8
1.4 Focus brand 8
1.5 Subjects 8
1.6 Content outline 8
2. Theoretical background 9
2.1 Health insurance choices 9
2.2 Conceptual framework 10 2.3 Attributes 11 2.3.1 Premium 11 2.3.2 Reimbursement 11 2.3.3 Health program 12 2.3.4 Service 13 2.4 Brand 14 2.4.1 Familiarity 14 2.4.2 Medical selection 14 2.4.3 Profit objective 15 2.4.4 Trustworthiness 15 2.4.5 Quality of care 15 2.5 Covariates 16 2.5.1 Product importance 16 2.5.2 Switching costs 16
2.5.3 Age, health, and income 17
2.5.4 Household composition and region 17
2.5.5 Mentality 18
2.5.6 Switching history and satisfaction 19
2.5.7 Supplemental insurance and voluntary deductible 19
3. Research design 19
3.1 Craft 19
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3.1.2 Realism of the stimuli 20
3.1.3 Validation 20 3.2 Measures 20 3.2.1 Attributes 20 3.2.2 None option 22 3.2.3 Choice sets 22 3.2.4 Brand perception 22 3.3 Subjects 23
3.3.1 Current health insurance 23
3.3.2 Sociodemographic covariates 26
3.3.3 Health-related covariates 26
3.3.4 Insurance-related covariates 27
3.4 Consumer behavior constructs 27
3.4.1 Product importance 28
3.4.2 Switching costs 28
3.5 Methods 28
3.5.1 Pseudo-R² 28
3.5.2 Likelihood Ratio Test 29
3.5.3 Market simulations 29
3.5.4 Segmentation 29
3.5.5 Information criteria and classification error 30
4. Results 31
4.1 Model performance 31
4.1.1 Pseudo-R²` 31
4.1.2 Likelihood Ratio Test 31
4.1.3 Predictive Validity 32 4.2 Model comparison 32 4.3 Model estimation 34 4.4 Applications 35 4.4.1 Relative willingness-to-pay 35 4.4.2 Market simulations 36 4.5 Segmentation 40 4.5.1 Attribute 3 40
4.5.2 Information criteria and classification error 40
4.6 Brand perception 41
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4.8 Model estimation 43
4.8.1 Total brand effect 44
4.9 Model performance 46
4.9.1 Pseudo-R² 46
4.9.2 Predictive Validity 46
4.9.3 Conclusion 46
4.10 Discussion of the segments 47
5. Conclusion & discussion 50
5.1 Conclusion 50
5.2 Limitations and further research 54
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1. INTRODUCTION
In 2006 the health insurance system in The Netherlands was drastically reformed by the introduction of a model with managed competition (Enthoven, 2007). This means that health insurers are provided with incentives to act as prudent buyers of care on behalf of their enrollees (Determann et al., 2016). Therefore, insurers are expected to compete on the dimensions (for example price and quality of care) that consumers value in order to maintain and increase their market share. Annually, consumers have the possibility to switch to another insurer's health insurance that better meets their preferences. In order to choose the most appropriate health insurance, consumers are expected to critically assess the available health insurances annually. Research of Vektis (2017) has shown that 6.4% of the Dutch population switched last year (2016-2017), representing 1.1 million consumers. In the years after the introduction of the new model in 2006 the switching percentage was lower as it was around 5% (Van der Schors, Brabers, and De Jong, 2017). This group and its behavior is interesting to study as insurers want to retain current customers and attract new customers.
1.1 Study background
Actual health insurance choices are widely studied. Although studying actual health insurance choices leads to new, valuable insights, there are several drawbacks. Firstly, only preferences that are observable from the available market data can be revealed (Determann et al., 2016). Secondly, Determann et al. (2016) mention that health insurance premiums are strongly regulated, which makes inferring willingness-to-pay from market observations hard or even impossible. In general, these revealed-preference studies (studies involving actual health insurance choices) do not provide insights in the relative importance of health insurance characteristics. Therefore, Determann et al. (2016) published an article on the relative importance of (Dutch) health insurance characteristics. They conducted a discrete choice experiment (DCE) to elicit and quantify consumer preferences and tradeoffs. A DCE is a stated-preference technique that originates from mathematical psychology (Luce and Tukey, 1964) and is grounded in random utility theory (Manski, 1977). Over the past years, the method has become increasingly popular in health economics (Clark et al., 2014). In DCEs, respondents are presented with a series of hypothetical scenarios (called choice sets) in which they are asked to choose between two or more alternatives that are distinguished from each other by systematically varying characteristics which are called attributes (Determann et al., 2016).
1.2 Research gap
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(2016) collected their data at the time of a government’s proposal allowing insurers to set a lower level of reimbursement of care by non-contracted providers. This proposal was heavily disputed by the medical profession and widely covered by the media (Determann et al., 2016). This may have biased their results, as they concluded that provider choice and associated reimbursement was the most decisive health insurance characteristic. Second, in the past years, multiple health insurers introduced a health program which should lead to a reduction in healthcare costs and add value to the insurance and the insurer’s brand. Health apps are a promising future direction for care (Robbins et al., 2017), but the effect of such programs on consumers’ preferences for an insurer that offers a health program has not been analyzed in previous research. Third, Determann et al. (2016) left a gap as they did not account for brand effects. Therefore, the aim of this study is quantifying consumers' trade-offs between (basic) health insurance (i.e. product) characteristics while accounting for brand effects. Therefore, the research question is:
What is the relative importance of product and brand characteristics in choosing a health insurance?
1.3 Brand effects
To measure brand effects, Eggers, Eggers, and Kraus (2016) created an extended choice-based conjoint analysis model with brand-specific covariates. This model with brand-specific covariates measures consumer responses to experimentally varied product configurations to separate the effects of product characteristics from the brand effect and dimensions of brand familiarity (Eggers et al., 2016), which is in line with concepts of the brand equity framework of Keller and Lehmann (2006).
1.3.1 Brand information
According to Keller's (1993) conceptual framework, familiarity with a brand is a necessary condition for both holding favorable, strong, and unique brand associations in memory and building customerbased brand equity. This additional value generated by a brand name relates to beneficial marketing outcomes such as a better image or lower price sensitivity (Keller, 2003). Branding literature shows that in situations of asymmetric and imperfect information, brands can serve as trust-building signals that deliver useful information to customers and therefore lower their perceived purchasing uncertainties (Eggers et al., 2016; Erdem and Swait, 1998). Kahneman and Tversky (1979) also showed that consumers tend to prefer the least uncertain situation when they are exposed to situations of both high and low uncertainty which have the same expected value. Thus, the more uncertainty a consumer perceives, the less likely a decision to purchase becomes.
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1.3.2 Information in health insurance choice process
Determann et al. (2016) describe the occurrence of asymmetric and imperfect information in the health insurance choice process, which is related to the model of managed competition. According to Determann et al. (2016), there is growing empirical evidence that many people are having trouble making optimal health insurance choices because they experience difficulties in understanding relevant health insurance differences. If consumers do not have the information and/or the cognitive abilities to adequately choose an insurance competition among health insurers may not yield the desired outcomes. In addition, substantial search and switching costs may be a barrier to adequate decision-making. Both are likely to be a major cause of consumer inertia, which is a preference for the status quo. According to Handel (2013), consumer inertia is typically observed in health insurance markets.
1.4 Focus brand
We developed a conceptual framework which takes these effects into account. A health insurance company in The Netherlands is used as focus brand in this thesis. Next to the main research question, multiple sub questions will be answered:
1. Which product and brand characteristics are important when choosing a health insurance? 2. How many actionable segments can be identified in the Dutch health insurance market
and on which dimension(s) do they differ?
3. How can the segments be defined in terms of preferences and demographic characteristics?
4. Are there any activities that the focus brand (Brand D) should put more focus on in order to create a competitive advantage?
5. Are there any activities that the focus brand (Brand D) should put less focus on or should not even participate in any longer?
1.5 Subjects
The study is based on a large, representative sample of the national adult population (n=433). This enables us to find out whether the consumer preferences differ according to sociodemographic characteristics.
1.6 Content outline
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going to use. In Chapter 5 we describe the conclusions, limitations, and suggestions for further research.
2. THEORETICAL BACKGROUND
In this chapter we provide a theoretical background of characteristics of health insurances that contribute to the health insurance choice process. Subsequently, we will formulate hypotheses based on prior studies.
2.1 Health insurance choices
As we aim to elicit and quantify consumer preferences and trade-offs, we will conduct a DCE. The first step in a CBC experiment is to carefully select the attributes and levels to be included in the experiment. This study involves five attributes: insurer, Attribute 1, Attribute 2, Attribute 3, and Attribute 4. This selection was based on a literature study including previous stated- and revealedpreference studies on the same topic. Also, it is based on the specifications of basic health insurances that are provided on insurers’ websites and comparison websites. Many consumers use those sources of information to make decisions; 49% of our respondents use comparison websites and 43.9% of them visit insurers’ websites or make phone calls. All comparison websites (for example Independer, Pricewise, and the Consumentenbond (Consumers Association)) communicate the insurer, the premium, and a statement about provider choice or reimbursement.
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increase in uncertainty means that a decision to purchase becomes less likely (Kahneman and Tversky, 1979). In this study we will assess the effects of brand and health programs, as these have not been analyzed in previous studies.
To determine which brand perception attributes should be analyzed, we examined insurers’ websites to find out which brand characteristics are communicated (as unique selling points) and thus likely to be perceived by consumers. In addition, we conducted interviews with experts in the field of health insurance (both researchers and employees of a health insurance company, n=4). This lead to a selection of five brand perception attributes: familiarity, perceived medical selection, perceived profit objective, trustworthiness, and quality of care. Previous findings on the effects of these characteristics will be discussed in Paragraph 2.4.
2.2 Conceptual framework
We analyze consumer choices between different product offerings (insurances). The theoretical framework for choice behavior is the random utility theory, which states that the overall utility U of individual i for an object j is a latent construct that includes a systematic component V and an error component ε, which catches all effects that are not systematic and consequently not accounted for (Manski, 1977; Eggers et al., 2016):
(1)
According to the random utility theory, consumers implicitly compare the utility of the choice options and choose the alternative that exhibits the highest utility (Eggers et al., 2016). In a general product choice context, it can be assumed that the overall utility V is a linear combination of the partworth utilities β of the brand b and other product attributes X:
(2)
In our context, we assume that the insurers differ in terms of Brand characteristic i1, Brand characteristic i2, Brand characteristic i3, Brand characteristic i4, and Brand characteristic i5. Consumers differ in their brand perception which is accounted for in the model by alternative-specific covariates. Also, effects will differs across segments s:
(3)
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i2, Brand characteristic i3, Brand characteristic i4, and Brand characteristic i5 on the overall utility of the health insurance and, hence, choice probability. With these additional components the model integrates objective product characteristics and subjective perceptions which is similar to the model of Eggers et al. (2016). The figure below shows the conceptual model:
Figure 1 | Conceptual model
2.3 Attributes
In this paragraph we will elaborate on the objective product characteristics of health insurances that were selected based on literature.
2.3.1 Premium
Health insurers are obliged to communicate their new premiums no later than November 12, seven weeks before the following year. Consumers need to stop their current insurance before January 1st and they can select a new health insurance until February 1st. Thus, consumers have seven weeks to evaluate their current health insurance and the alternatives. Usually, the major insurers communicate their new premiums only shortly before the deadline, as they wait for each other to announce the premium. This enables the last parties to make small adjustments in order to obtain a large(r) market share. In addition, this results in beneficial premiums.
Van der Schors, Brabers, and De Jong (2017) identified the premium of the health insurance as the most important reason for switching. Also according to Strombom, Buchmueller, and Feldstein (2002), consumers are, on average, quite sensitive to price. Their results indicate substantial variation in price sensitivity related to expected health care costs: younger, healthier people are between two and four times more sensitive to price than people who are older and less healthy. Determann et al. (2016) found similar results: monthly premium was the most important determinant for young, healthy, and lower income respondents. This effect is described in hypothesis 1:
H1a: The lower the monthly premium of the health insurance, the more likely consumers will be to purchase the health insurance.
H1b: The effect of the monthly premium of the health insurance on consumers’ preferences varies across segments.
2.3.2 Reimbursement
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system (Bes et al., 2013). However, as those insurers received negative publicity and feared reputation damage, they included the providers in their network later on (NZa (Dutch Healthcare Authority), 2007). Subsequently, insurers introduced insurances with differentiated reimbursement levels for contracted and non-contracted providers. This is a negative financial incentive to visit non-contracted providers. Typically, its actual impact is very small as insurers usually contract more than 95% of all providers. Thus, the level of provider choice (percentage/number of fully reimbursed providers of care) in The Netherlands is mostly determined by the level of reimbursement for services by noncontracted health care providers. Therefore, we decided to use the attribute reimbursement in our study.
Over the years, the number of people enrolled in an insurance with differentiated reimbursement levels increased. According to the NZa (Dutch Healthcare Authority) (2009), in 2009 only 28% of all enrollees still have an insurance that does not differentiate reimbursement between contracted and non-contracted providers (reimbursement is always 100%, regardless of contract). Of all people who enrolled in a new insurance via Independer (The Netherlands’ largest comparison website) in 2015 (for 2016), 25% chose a non-differentiating insurance, but in 2017 less than 15% chose this type of insurance for 2018 (am:signalen, 2018).
The model of Determann et al. (2016) showed that being able to choose a care provider freely was by far the most decisive characteristic for respondents aged over 45, those with chronic conditions, and those with a gross income over €3000/month. This leads us to hypothesis 2:
H2a: The higher the level of reimbursement of the health insurance, the more likely consumers will be to purchase the health insurance.
H2b: The effect of the level of reimbursement of the health insurance on consumers’ preferences varies across segments.
2.3.3 Health programs
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As both the development and the maintenance of a loyalty program is costly for an organization, it is useful to examine whether the additional value of the program is considered in consumers’ purchase decisions. The goal of the programs is twofold. On the one hand, a health program should add value to the insurance and the insurer’s brand. On the other hand, a health program should lead to a reduction in healthcare costs as insurers need to anticipate the trend; according to a report of the RIVM (National Institute for Public Health and the Environment) (2017), in 2040 the healthcare costs in The Netherlands will be doubled to an amount of 174 billion euros. Also Ernsting et al. (2017) see chronic conditions as an increasing challenge for both individuals and the healthcare system. They suggest that smartphones and health apps are potentially promising tools to change health-related behaviors and manage chronic conditions. In addition, Carroll et al. (2017) saw that mobile phone use and the adoption of healthy lifestyle software (health apps) are rapidly proliferating. Although there were many smartphone and health app users, a substantial proportion of the population was not engaged (Ernsting et al., 2017). Carroll et al. (2017) found that the main users of health apps were individuals who were younger, had more education, reported excellent health, and had a higher income. The findings of Ernsting et al. (2017) also suggest age-related, socioeconomic-related, literacy-socioeconomic-related, and health-related disparities in the use of mobile technologies. Although differences persist for gender, age, and educational attainment, many individual sociodemographic factors are becoming less potent in influencing engagement with mobile devices and health app use (Carroll et al., 2017). In addition, app use was associated with intentions to change diet and physical activity and meeting physical activity recommendations (Carroll et al., 2017; Ernsting et al., 2017). Also, Ernsting et al. (2017) advise app developers and researchers to pay attention to the needs of older people, people with low health literacy, and chronic conditions. Thus, it is assumed that 1) availability of a health program and 2) the degree of personalization of the health program affect preferences. This effect is described in hypothesis 3:
H3a: If the insurer offers a health program, consumers will be more likely to purchase the insurer’s health insurance.
H3b: The more personalized the health program, the more likely consumers will be to purchase the health insurance.
H3c: The effect of a health program on consumers’ preferences varies across segments.
2.3.4 Service
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H4a: The higher the level of service of the health insurance, the more likely consumers will be to purchase the health insurance.
H4b: The effect of the level of service of the health insurance on consumers’ preferences varies across segments.
2.4 Brand
In this paragraph we will elaborate on the subjective brand characteristics of health insurers that were selected based on literature.
2.4.1 Familiarity
Previous studies indicate a negative correlation between information search and familiarity. Thus, Biswas (1992) noted that consumers recognized a time saving since less time was spent shopping for familiar brands. Later, Kent and Allen (1994) demonstrated that familiar brand names were expected to have a competitive advantage over less familiar brands because of superior recall of information about familiar brands. Thus, in order to improve the likelihood of a sale, new firms are required to increase familiarity, maximize customer knowledge, and lower prospective customers’ perceived uncertainty (Eggers et al., 2016). Arora and Stoner (1996) studied the effect of familiarity on service selection outcomes. In the insurance service area, respondents indicated that they were more likely to use the high name familiarity insurance company than they were to use the low name familiarity company. This effect is described in hypothesis 5:
H5: The higher consumers’ knowledge of the insurer, the more likely they will be to purchase the insurer’s health insurance.
2.4.2 Medical selection
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A medical selection may evoke different responses, as it appeals to the system’s solidarity. Some people appreciate the fact that healthcare costs are paid together, as a treatment for a seriously ill person is often unaffordable for an individual. Others do not want to pay for someone else’s healthcare costs (when this person is less healthy). This leads to hypothesis 6:
H6: The degree of perceived medical selection significantly affects the purchase of the insurer’s health insurance.
2.4.3 Profit objective
Most health insurers do not have a profit objective as those are part of cooperatives. According to Minister Schippers of Public Health, 98% of all enrollees in The Netherlands has a health insurer without profit objective (Pricewise, 2013). The cooperatives, insurers without profit objective, are allowed to make a profit which can be invested in healthcare, premium reduction, or serve as a financial buffer (Pricewise, 2013). Some insurers use their origin as a cooperative as a unique selling point in their communication, e.g. “Coöperatie VGZ” (Cooperative VGZ). This might influence brand associations in terms of favorability, strength, and uniqueness as consumers are often concerned about the large profits that are made by insurers. This effect is described in hypothesis 7:
H7: The more consumers think the insurer has no profit objective, the more likely they will be to purchase the insurer’s health insurance.
2.4.4 Trustworthiness
As described previously, insurers are reluctant to implement selective contracting, as they believe their enrollees will not accept this. According to Bes et al. (2013), one reason is that enrollees do not trust their health insurer. In the study of Bes et al. (2013), trust in the health insurer turned out to be an important prerequisite for the acceptance of selective contracting among their enrollees. In addition, Balkrishnan et al. (2003) found that higher trust was significantly associated with increasing years of enrollment with the insurer and higher adequate choice in insurer selection.
H8: The more consumers consider the insurer as trustworthy, the more likely they will be to purchase the insurer’s health insurance.
2.4.5 Quality of care
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(Determann et al., 2016). To date, however, insurer-provider negotiations are mainly focused on price and volume rather than on quality (Determann et al., 2016). According to Brabers, Reitsma-van Rooijen, and De Jong (2012), this is at least partly caused by the absence of reliable quality indicators.
However, all respondents of the study of Determann et al. (2016) preferred selective contracting that was primarily focused on quality of care over selective contracting focused on price of care. Also, research showed that older consumers are more sensitive to quality compared to younger consumers, who are more sensitive to premium (Boonen, Laske-Aldershof, and Schut, 2016; Brabers et al., 2012; Reitsma-van Rooijen, Brabers, and De Jong, 2015). Also, the model of Determann et al. (2016) distinguishes a class that is quality minded that involved 12% of the respondents. Therefore, they hope insurers will be able to provide objective quality information of the contracted providers that is easy to understand, consumers might make more well-considered insurance choices that do include quality of contracted care. This leads to the following:
H9: The more consumers think the insurer guarantees a high quality of care, the more likely they will be to purchase the insurer’s health insurance.
2.5 Covariates
In this paragraph we will elaborate on a set of constructs and variables that are likely to influence our health insurance choice context. These were selected based on literature.
2.5.1 Product importance
Customer choice behavior can differ between products based on the importance of the product to the customer (Eggers et al., 2016). Thus, product importance can be a covariate in the model of the relationship between customer uncertainty and the decision that is made (Bloch and Richins, 1983). This leads us to the following:
H10: The degree of product (i.e. health insurance) importance significantly affects the purchase of the insurer’s health insurance.
2.5.2 Switching costs
There is a growing interest among economists in markets where it is costly for consumers to switch among competing suppliers. Kim and Son (2009) define switching costs as “the extent to which a customer feels dependent on a service because of economic, social or psychological investments that would become useless in other services”.
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insurances. Health care is defined as an experience good, which implies that consumers will have better information on the quality of their current insurance than on the quality of its competitors (Strombom et al., 2002). Klemperer (1995) argues that this information asymmetry makes insurance changes costly for risk-adverse individuals. In addition, because health insurances vary in their rules and procedures, there are costs associated with learning a new system once someone changes insurances. According to Strombom et al. (2002), the one type of switching costs that is unique to health care is arguably the most important. Consumers who change insurances often must sever relationships with previous health care providers and begin relationships with new ones. This link between providers and insurances generates greater “brand loyalty” than that which occurs in other markets. However, even when switching insurances does not require changing health care providers and transaction costs are low, consumers may stay in the same health insurance despite changes in the factors that influenced the initial choice. Thus, persistence may also result from apparent deviations from rational behavior (Samuelson and Zeckhauser, 1988). This leads to hypothesis 11:
H11: The degree of perceived switching costs significantly affects the purchase of the insurer’s health insurance.
2.5.3 Age, health, and income
In addition to the choice model, Determann et al. (2016) fitted a class assignment model to test whether class membership is dependent on age, health status and income. These three variables were selected based on literature (Boonen et al., 2016; Brabers et al., 2012; Gruber and McKnight, 2016; Reitsma-van Rooijen et al., 2015). They found that class membership is indeed dependent on age, health status, and income.
In addition, Boonen et al. (2016) showed that young people are more sensitive to price, whereas older people are more sensitive to quality. Also, young people switch more often than older people in 2017 and in prior years (Van der Schors et al., 2017). Thus, behavior and preferences differ according to age.
As users of health apps mainly reported excellent health (Carroll et al., 2017), we expect that class membership is also dependent on health program use.
2.5.4 Household composition and region
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Since health insurers used to operate locally before the reform of the health insurance system in 2006, region is another variable that is likely to affect consumers’ preferences. It is known that only a small share of the Dutch population switched to another insurer one or multiple times since 2006. This indicates that many people stayed with their (local) insurer. Thus, we analyze whether preferences differ according to the region where the respondent lives.
2.5.5 Mentality
Mentality is a segmentation that was developed by research agency Motivaction. Target groups are often defined based on sociodemographic data such as age, gender, or education level. However, people with similar demographic data could belong to different target groups. Mentality distinguishes target groups by looking at people’s underlying values: “What is important in your life?”. The model of Motivaction (2018) distinguishes three segments: Pragmatic (46%), Less Self-reliant (45%), and Socially Critical (9%).
The first segment, Pragmatic, involves four subtypes:
• Cosmopolites who are critical world citizens who integrate postmodern values such as development and experience with modern values such as success, materialism and enjoyment. • Career-oriented individualists with a strong fascination for social status, new technology, risk
and tension.
• Pioneers of the experience culture, in which experiment and breaking with moral and social conventions have become goals.
• The liberal-conservative social upper class that embraces technological development and opposes social and cultural changes.
The second segment, Less Self-reliant, involves three subtypes:
• The moralistic, dutiful and status quo-oriented bourgeoisie that holds on to traditions and material possessions.
• The conformist, status-sensitive bourgeoisie who seeks the balance between tradition and modern values such as consumption and enjoyment.
• The impulsive and passive consumers who first and foremost strives for a carefree, enjoyable and comfortable life.
The third and last segment, Socially Critical, can be described as follows:
• The socially critical idealists who want to develop themselves, take a stand against social injustice and stand up for the environment.
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2.5.6 Switching history and satisfaction
Frank and Lamiraud (2009) compared the health insurance choices of new enrollees (switchers) to insurance choices of those who kept their previous insurances (non-switchers). They found that people who switched insurances paid lower premiums than those that stayed in the same insurance. Also, they found evidence that suggests some quality differences affected choice behavior: 29% of switchers opted for firms having reserves below the required level, versus 12% of non-switchers. As switchers seem to behave differently, we analyze the effect of switching history as a covariate. Determann et al. (2016) found that the most common reason not to switch to another health insurance is ‘being satisfied with current insurance’. Also, many respondents of the study of Frank and Lamiraud (2009) explicitly reported that they stay with their health insurance because they are satisfied with their arrangement (79%). Thus, satisfaction is an important driver of choices and therefore we analyze it as a covariate.
2.5.7 Supplemental insurance and voluntary deductible
Determann et al. (2016) asked their respondents to what extent a supplemental insurance affects their choice for a basic health insurance and 60.8% answered that it is affected ‘much or very much’. As we expect that preferences regarding supplemental insurance will affect choice in our study, we include it as a covariate.
It has not been analyzed to what extent a voluntary deductible affects choice, but we expect this characteristic to behave similarly as it also is an aspect of someone’s current health insurance that affects premium. Therefore, we also include current voluntary deductible as a covariate.
3. RESEARCH DESIGN
In this study we will conduct a choice-based conjoint experiment. In this chapter we will describe this method and the data that we will use.
3.1 Craft
The choice sets are presented that is very similar to the presentation of insurances on comparison websites to create a realistic choice setting and enhance external validity. Therefore, in this study previous findings of Wlömert and Eggers (2014) on the effects of craft in choice-based conjoint (CBC) formats were taken into account.
3.1.1 Ceteris paribus instruction
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choice tasks (Allenby et al., 2014). These instructions are called ceteris paribus instructions. If respondents are not provided with ceteris paribus instructions, they might infer unobserved characteristics to be correlated with the attributes that are varied (Bradlow, Hu, and Ho, 2004). Therefore, the following phrase is used in the first choice set:
Please assume that you already found a supplemental insurance which can be combined with each of the following basic health insurances. Any discounts have already been included in the premiums.
3.1.2 Realism of the stimuli
Past research suggests that rich visual representations are more realistic than text and more likely to evoke marketplace-like responses from respondents (Dahan and Hauser, 2002). Dzyabura,
Jagabathula, and Muller (2016) suggest that text-based profiles lead to different partworths than morerealistic products. It is likely that this aspect of craft is less critical in the presentation of an insurance compared to the smartwatches in the study of Eggers, Hauser, and Selove (2017). They chose this product category because they believed it would provide a reasonable test of whether four aspects of craft affected observed scale. Nevertheless, our choice sets were not just text-based profiles. They were made visually attractive and realistic by the inclusion of the insurers’ logos.
3.1.3 Validation
Two holdout choice tasks were used to compute hit rates. The holdout tasks were placed in the middle of the choice sets and were similar to those choice sets used for estimation; respondents were unaware these choice tasks were for internal validation.
Eggers, Hauser, and Selove (2017) see external validation as a greater challenge. They strive to a test of whether the CBC model predicts the choices consumers would make if the hypothetical profiles became real products in the marketplace. External validation tasks of CBC are rare in the literature. However, this task can be considered reasonably close to external validation.
3.2 Measures 3.2.1 Attributes
This study involves five attributes: insurer, Attribute 1, Attribute 2, Attribute 3, and Attribute 4. The five attributes are explained in the table below:
Attribute Explanation
Insurer (logo) The organization that offers the basic insurance
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Attribute 2 The percentage of the average treatment rate at non-contracted healthcare providers that is reimbursed
Attribute 3 The stimulation of a healthy lifestyle by the insurer
Attribute 4 The score regarding service in the Healthcare Monitor (Zorgmonitor) of the Consumers Association (Consumentenbond)
Table 1 | Attributes and explanations of the conjoint experiment
The Dutch health insurance market has four big players: Achmea, VGZ, CZ, and Menzis. All of these concerns offer multiple labels/brands and together these concerns have a market share of 90%
(Lastenvrij.nl, 2017): Achmea is the largest with 30%, VGZ has 25%, CZ has 20%, and Menzis has 10%. The concern Achmea does not offer (health) insurances under the concern’s name, their largest label is Zilveren Kruis, which has a market share of 20.5% (Vektis, 2017). As this study examines the value of brands, it is useful to make a selection of brands that represents a large share of the market. On the other hand, it is interesting to compare big players with a smaller brand. DSW is such a smaller insurer. Lastly, a fake brand is included as a level of the attribute insurer: GMK. As this brand is empty, free of associations, we can assume it has no brand value. Therefore, this brand can serve as a reference level to assess the value of the other brands. The name GMK is chosen because of its neutrality: it does not imply any particular focus like low prices, high service, or a specific region of origin which is sometimes mentioned in insurers’ names. Also abbreviations are widely used in their names, but those are more neutral. The logo of GMK is colored blue, as this is an unobtrusive color which is regularly used in insurers’ logos.
The importance and potential effects of the attributes have been discussed in Chapter 2. Both the levels of the Attribute 1 and Attribute 2 were based on health insurances that are currently available on the market. The same holds for Attribute 3. The extended health program is similar to SamenGezond (offered by Menzis) and Actify (offered by Zilveren Kruis). The limited health program resembles programs that are sometimes offered by employers. The scores for Attribute 4 were retrieved from the Healthcare Monitor (Zorgmonitor) of the Consumers Association (Consumentenbond). As the scores varied from 7.2 to
8.1 (out of 10), this range is chosen for the levels of the attribute service. 7.6 was the average score, which is the middle level of the attribute. The table below shows the levels of all attributes besides the attribute insurer:
Attribute Level 1 Level 2 Level 3
Attribute 1 €95 €105 €115
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Attribute 3 No program Limited: “Weekly new
general lifestyle tips for a healthier life by email”
Extended: “An online health program (app and website) that provides insight into your health and personal advice for a healthier life”
Attribute 4 7.2 7.6 8.1
Table 3 | Levels of attributes
3.2.2 None option
The none option is included as a separate question below the choice set: “If I have to choose between these insurances and my current basic insurance, I would stay with my current insurer”, Yes/No. This statement is considered as none option, as it represents the status quo. This dual-response choice design is recommended when consumers might choose “none” to avoid difficult decisions (Eggers, 2015). If the none option would be included as an alternative, we would not have information on preferences if a consumer chooses “none” in every set. Our design stimulates the respondents to elaborate on every choice set and it forces them to make a choice between two options. However, we do want to know to what extent the respondents are interested in the option that they selected: do they consider that option as more attractive than their current insurance? This information will be used to assess the willingness-to-pay of existing insurances: at which price does an existing insurance become more attractive than (an average) current insurance?
3.2.3 Choice sets
Previously, we discussed our considerations in the design of the choice sets. As it is quite a complex choice task, respondents will be presented with only two alternatives per choice set. Respondents are asked to evaluate 15 choice sets, as this number of choice sets enables us to show every insurers three times and every level of the other attributes five times. The stimuli were allocated randomly to the choice sets and controlled for the efficiency criteria of level balance, orthogonality, minimal overlap, and domination (Eggers, 2015). Also, from a respondent’s perspective this number of choice sets is considered reasonable since the choice sets include only two alternatives. According to Eggers (2015), a researcher needs to motivate respondents to evaluate more than twelve choice sets, therefore the respondents received a small financial incentive.
3.2.4 Brand perception
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attribute insurance. Therefore, the respondents were asked to rate brand-specific constructs. These ratings are important for the estimation of the extended model and for testing of the hypotheses. The table below shows the brand-specific constructs:
Construct Operationalization Scale
Brand characteristic i1 How well do you know the following insurers?
1 = not at all; 5 = very well
Brand characteristic i2 To what extent is the following statement applicable to the insurers below?
“This insurer requires no medical selection; everyone is welcome at this insurer”
1 = totally not applicable; 5 = totally applicable; and 6 = I do not know
Brand characteristic i3 To what extent is the following statement applicable to the insurers below?
“This insurer has no profit objective”
1 = totally not applicable; 5 = totally applicable; and 6 = I do not know
Brand characteristic i4 To what extent do you consider the following insurers as trustworthy?
1 = totally not trustworthy; 5 = extremely trustworthy; and 6 = I do not know
Brand characteristic i5 To what extent do you expect to receive qualitatively good care at the following insurers?
1 = moderate quality of care; 5 = excellent quality of care; and 6 = I do not know
Table 4 | Operationalization of brand perception constructs
3.3 Subjects
The survey was sent to a representative sample of the Dutch population. Therefore, the study was conducted with a Dutch questionnaire. We questioned a stratified sample based on age, gender, education level and income. A total of 433 respondents completed the survey. The sample consisted of 49.2% male, and 50.8% female respondents. The survey involves consumers from 18 to 75 years old, since everyone over the age of eighteen is required to have health insurance. In addition, allowing people over the age of 75 to be in the sample would result in a number of respondents that is too small to be representative.
3.3.1 Current health insurance
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slightly larger: 16.4%. 8.7% of the respondents is insured at Menzis, but also Menzis’ market share is larger: 10.4%. DSW is the insurance company of 3.3% of the respondents, which is very similar to their market share of 3%.
Figure 3 | Current insurer of respondents
The second question asks the monthly premium that is paid for the current basic insurance. The largest share of respondents (36.7%) pays a monthly premium of €100-110, which is also the median.
Figure 4 | Current premium of respondents
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Figure 5 | Current reimbursement of respondents
Also, the respondents were asked how likely it is that they will stay with their insurer of 2017 after January 1st 2018. On average, respondents report a 7.3 to indicate this likelihood. In Net Promoter Score (NPS) research, only the respondents who report top-2 or -3 numbers, 9 and 10 or 8, 9 and 10, are identified as people who will take action (Reichheld, 2003). If we apply this theory to this question, only people who reported a 0, 1, and probably also people who reported a 2 will not stay with their insurer of 2017 in 2018, which is 12.4% of the respondents. Which is a higher percentage than the market switch of 2016-2017 which was only 6.4% (Vektis, 2017). This discrepancy could be explained in two ways: 1) the market switch will be higher this year, or 2) people do not always act in line with their intentions. This phenomenon is described as the intention-behavior gap (Snienotta, Scholz, and Schwarzer, 2005). A meta-analysis by Sheppard, Hartwick and Warshaw (1988) reported a correlation of .53 between intention and behavior, which confirms the discrepancy between intention and actual behavior.
Figure 6 | Respondents’ intention to stay with current insurer
,8% 3 3,2% 8,3% 22,4% 20,5% ,3% 1 4,5% 0,0% 35,9% 0% % 10 % 20 % 30 40% Less than % 65 65% 70% 75% 80% 85% 90% 95% 100%
Current reimbursement (n=156; 36%)
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% is unknown
,0% 9 ,6% 1 1,8% 1,6% 1,4% ,4% 7 6,5%10,6% ,7% 12 11,8% 35,6% % 0 % 5 % 10 % 15 % 20 % 25 % 30 % 35 % 40
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Finally, we know the sources of information when the respondents plan to subscribe to a new health insurance. Figure 7 shows that comparison websites are consulted most often; almost half of the respondents (49%) visits comparison websites. In addition, many respondents visit insurers’ websites or make phone calls (49.3%).
Figure 7 | Respondents’ sources of information during choice process
3.3.2 Sociodemographic covariates
As household composition might differ across segments, the study accounts for variation in this variable by including it in the model as a covariate. Most of the respondents, 35.6%, live with a partner, also many of them, 31.2%, live with a partner and (a) child(ren), 28.2% of the respondents lives single, and only 5.1% is single and living with (a) child(ren).
Region is another variable that might affect consumers’ preferences. Many respondents, 30.7%, live in the West of the country, 27% of them live in the South, 18.2% lives in the East, 10.6% of the respondents live in one of the three largest cities (Amsterdam, Rotterdam or The Hague), 9.7% lives in the North and 3.7% lives in the suburbs.
Of 431 respondents (out of 433) the Mentality is known. A large share of 46.4% of the sample belongs to the group that is called Pragmatic. The group of Less Self-reliant people consists of 43.4% of the sample. The Socially Critical group is small and consists of only 10.2% of the respondents.
3.3.3 Health-related covariates
The respondent were asked to grade their health status on a scale from 1 to 10 (1 = very unhealthy; 10 = very healthy). Thus, health status was self-reported. On average respondents give their health a 7.15 (n=433) with a standard deviation of 1.58. In addition, respondents were asked whether they use a health program (app or wearable like Runkeeper or Fitbit). 19.2% of the respondents (n=433)
,0% 49 43,9% ,2% 16 ,9% 3 5,5% ,8% 29 0% % 10 20% % 30 % 40 % 50 % 60 Comparison websites Visit website / call insurer Ask family / friends
Ask GP Other Not
applicable, since I will not switch
Sources of information (n=433)
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answered this question positively, which indicates that a vast majority of 80.2% does not participate in such a health program yet.
3.3.4 Insurance-related covariates
The respondents were asked how often they switched to another insurer during the past five years. A majority of them (60%) did not switch during the past five years, 24.7% switched only once and a smaller group switched multiple times: 5.8% switched twice during the past five years, 4.6% switched three times, 2.3% switched four times and 2.5% switched every year, namely five times. This variable is included in the model as a covariate since it might explain a preference for the none option, e.g. staying with one’s current insurer. Another variable that might explain choice is satisfaction with one’s current insurer, which was measured on a scale from 1 to 5 (1 = very unsatisfied; 5 = very satisfied). On average, the respondents are quite satisfied with their current insurer; the mean is 4.05 (n=433) with a standard deviation of .86). As mentioned previously, satisfaction is an important driver of loyalty, so a high score for satisfaction is likely to cause a preference for the none option.
Supplemental insurances and voluntary deductibles can also be considered as insurancerelated covariates as they can make an insurance more complex, so these factors can affect preferences and inhibit switching intentions. Supplemental insurances involve certain coverages and premiums, and voluntary deductibles involve particular premium discounts. Many people have one or multiple supplemental insurances (72.3%; n=433). 25.4% of the respondents does not have this kind of insurance and 2.3% does not know it. Not many people have a voluntary deductible; only 21% of the respondents have a voluntary deductible that varies from €100-500. 73.4% does not have a voluntary deductible and 5.5% does not know. Of the people who do have this voluntary deductible, a large majority of 70.3% chose the highest amount of €500. 9.9% chose the amount of €100, 11% chose €200, 7.7% chose €300, and only 1.1% of the people who have a voluntary deductible chose the amount of €400.
3.4 Consumer behavior constructs
The constructs product importance and switching costs are both measured by multiple items.
Therefore, the scales need to be assessed by calculating the reliability coefficient (Cronbach’s Alpha). This score is calculated over the sum of the items and is also called the coefficient of internal consistency (Cortina, 1993). High values (>.80) indicate a high reliability or high internal consistency, which means that the merged items measure the same concept. Values below .50 indicate insufficient reliability and in general a scale with a value higher than .70 is considered reliable.
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3.4.1 Product importance
To measure product importance we used the scale of Eggers et al. (2016) and constructed an index of these items and an additional item: I compare my health insurance with insurances of other providers every year. Thus, this scale initially consisted of four items with scales ranging from 1 to 5:
• I am interested in health insurances
• I think it is important to find the best health insurance that matches my needs • I regret a bad decision regarding a health insurance [deleted]
• I compare my health insurance with insurances of other providers every year
The reliability coefficient of this scale was .650. However, by deleting the third item (I regret a bad decision regarding a health insurance), the coefficient would increase to .686. This value is considered sufficiently high to conclude that the items measure the same concept. Therefore, the third item is deleted. The mean of the construct product importance is 3.16 (1 = low importance; 5 = high importance) with a standard deviation of .95.
3.4.2 Switching costs
To measure switching costs we used the scale of Kim and Son (2009) which also consisted of four items with scales ranging from 1 to 5:
• Switching to a new health insurance would involve some hassle • Some problems may occur when I switch to another health insurance • It is complex for me to change health insurance
• If I leave this health insurer, I will waste the effort that I have made in the application for this health insurer
The reliability coefficient of the scale to measure switching costs was .839, which is a high value that indicates a high reliability and internal consistency. The mean of the construct switching costs is 2.77 (1 = low switching costs; 5 = high switching costs) with a standard deviation of 1.03.
3.5 Methods 3.5.1 Pseudo-R²
To find out how well the model fits and predicts the observed choices, the Pseudo-R² and adjusted Pseudo-R² will be calculated using the following formulas:
(4)
(5)
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with m = number of alternatives per choice set J n = number of consumers c = number of choice sets per consumer
3.5.2 Likelihood Ratio Test
To analyze whether the estimation model is better than the null model, the Likelihood Ratio Test will be performed. The test statistic follows a chi-squared distribution:
(7)
with H0 = There are no differences between the models.
3.5.3 Market simulations
The absolute willingness-to-pay can be calculated by another method: market simulations. It involves the construction of competitive scenarios and prediction of purchase probabilities that represent preference shares or market shares. An advantage of this method is that the results are expressed in terms that are actionable and make sense to management.
These market simulations involve some assumptions that should be taken into account (Eggers, 2015). The first assumption is that all attributes that affect buyer choices in the real world have been accounted for. The second is that consumers in the real world are aware of all available alternatives and the third assumption is that there are no switching costs.
First, we create a scenario with an offer of Brand D and the none option. It will show the absolute willingness-to-pay for an average consumer to consider buying the current insurance of Brand D relative to the none option. Therefore, the willingness-to-pay that we will find is called the consideration willingness-to-pay. We will calculate the average choice share i.e. market share for the current insurance of Brand D and the none option using the Multinomial Logit (MNL) model. Accordingly, an object j from a choice set with J alternatives is represented by the MNL model in terms of choice probabilities prob:
(8)
3.5.4 Segmentation
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in tastes into account. A mixture model involves a choice model and estimation procedure that account for heterogeneity. Mixture models assume that utilities are distributed across consumers according to the mixing distribution: . This distribution involves assumptions about . Either consumers belong to discrete segments that differ in preferences: finite mixture (“Latent Class”), or their preferences are represented by a (normal) distribution: continuous mixture (“Hierarchical Bayes”). Thus, one can distinguish three models: an aggregate-level model, a segmentlevel model, and an individual-level model. In this study, a segment-level model is developed. This model assumes homogenous segments that differ in their preferences and all respondents are allocated to the segments with a certain probability. The result is an analysis per segment with a logit model. The optimal number of segments is not known prior to the analysis and is not retrieved by the estimation method. Therefore, estimating models for several numbers of segments is a good solution. Subsequently, the best fit is found according to log-likelihood-based measures (information criteria), classification error and interpretability of the models. These steps were repeated multiple times to see if the solution was stable, since Latent Class estimation might identify a local optimum only (Eggers, 2015).
3.5.5 Information criteria and classification error
The information criteria AIC, BIC, and CAIC do not only assess the model fit, they also take the number of parameters into account; the Log Likelihood is penalized for the number of parameters. They can be calculated using the following formulas:
(9)
(10)
(11)
with N = sample size
The model with the minimum AIC, BIC, or CAIC should be chosen. The BIC and CAIC are almost identical and have higher penalties for complexity, which increases with the number of latent classes. These criteria are preferred, especially for large sample sizes as in this study (Eggers, 2015). The AIC is useful for small sample sizes, but the penalty of the AIC is often too small. This criterion tends to favor more complex models (i.e. more latent classes) which also occurs in this study; the value of the AIC keeps becoming smaller as the number of latent classes increases. The classification error is the average of the minimum probability that a respondent belongs to a particular class across all respondents. Obviously, the classification is better if the segments are strongly separated, so the probability that a case belongs to a particular class is close to either 0 or 1.
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4. RESULTS
In this chapter we will describe the model-building process and discuss the results of the models. Firstly, we will specify and estimate an aggregate model. Secondly, applications like willingness-topay and market simulations are discussed. Thirdly, we will specify and estimate an LCM which includes the brand perception attributes and covariates. Finally, the segments and their differences are discussed.
4.1 Model performance 4.1.1 Pseudo-R²
The first step of the analysis is an aggregate, partworth model for all attributes: insurer, Attribute 1, Attribute 2, Attribute 3, and Attribute 4. To find out how well the aggregate model fits and predicts the observed choices, the Pseudo-R² and adjusted Pseudo-R² are calculated.
Model LL Parameters Pseudo-R² Adjusted
Pseudo-R²
Null -9004.02 0 0 0
Partworth -7347.17 13 .184 .183
Table 5 | Pseudo R² of the partworth model
The Pseudo-R² lies between 0 and 1 and can be quite small, usually .2 to .4 can be considered acceptable (Eggers, 2015). As the Pseudo-R² of our model is .184, we need to improve the model.
4.1.2 Likelihood Ratio Test
Next, the Likelihood Ratio Test can be performed to analyze whether the estimation model is better than the null model.
Model Chisq df Critical value
Null 3313.7 13 > 27.688 (α=.01)
Partworth
Table 6 | Likelihood Ratio Test for the partworth model
Thus, there are significant differences between the models (p < .001) and the estimated parameters are significantly different from zero. Therefore, we can reject the null hypothesis and we will proceed with the partworth model.
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4.1.3 Predictive Validity
Based on the two holdout choice sets, the predictive validity of the model is assessed. Holdout choice sets are choice sets that are not used for estimation. The alternatives of this choice set are equal for all respondents, which offers the possibility to find out how good estimates can predict respondents’ actual choices. Overall, 9575 (7443 + 2132) of the total 12.990 observed choices are predicted correctly, which is a hit rate of 73.71%.
Prediction Table Estimated Observed 1 2 Total 1 7443 1088 8531 2 2327 2132 4459 Total 9770 3220 12990
Table 7 | Hit rate of the partworth model
4.2 Model comparison
Obviously, the goal is to find the best model. A good and common way to find this model is to start with a partworth model and change one attribute at a time. First, we will analyze whether the effect of Attribute 1 is linear.
Model LL Parameters
Partworth -7347.17 13
Attribute 1 linear -7350.22 12
Table 8 | Log-likelihood values (1)
Subsequently, the question is whether the differences in LL are significant. This can be calculated using the Likelihood ratio test.
Model Chisq df Critical value
Partworth 6.1 1 < 6.635 (α=.01)
Attribute 1 linear
Table 9 | Likelihood Ratio Test for model with Attribute 1 as linear attribute
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because the levels are numerical values on a scale from 1 to 10. This could further decrease the number of parameters.
Model LL Parameters
Attribute 1 linear -7350.22 12
Attr 1 & 4 linear -7350.24 11
Table 10 | Log-likelihood values (2)
Model Chisq df Critical value
Attribute 1 linear .04 1 < 6.635 (α=.01)
Attr 1 & 4 linear
Table 11 | Likelihood Ratio Test for model with Attribute 4 as linear attribute
The decrease in fit is not significant if Attribute 4 is treated as linear. Again, a linear model provides the same fit as a nominal model but is more parsimonious. Therefore, it is recommended to proceed with the linear model for Attribute 1 and Attribute 4. Next, we will analyze whether the effect of Attribute 2 is linear, because the levels of this attribute are percentages and the utilities could be related linearly.
Model LL Parameters
Attr 1 & 4 linear -7350.24 11
Attr 1, 4, and 2 linear -7364.49 10
Table 12 | Log-likelihood values (3)
Model Chisq df Critical value
Attr 1 & 4 linear 28.5 1 > 6.635 (α=.01)
Attr 1, 4, and 2 linear
Table 13 | Likelihood Ratio Test for model with Attribute 2 as linear attribute
There are significant differences between the models (p < .001). Thus, additional parameters result in an increase in fit and the partworth model for Attribute 2 fits significantly better. Therefore, it is recommended to proceed with the linear model for Attribute 1 and Attribute 4 and the partworth model for Attribute 2. Next, we will analyze whether the model improves when Attribute 3 is deleted, as its effect is insignificant in all of the previous models.
