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Seven reasons to choose metric conjoint analysis over choice-based conjoint analysis

Metrisim
by Craig F. Kolb

This is a revision of an article I released in 2021.

Conjoint analysis is usually divided into two broad types: traditional conjoint analysis (CA) and Choice Based Conjoint (CBC) - sometimes referred to as Discrete Choice Modelling (DCM).

Traditional conjoint analysis uses one of either rating (metric), ranking or pairwise forms of data collection, while CBC uses choices. The profiles can either be in a full or partial profile form.

In the 90s software vendors started promoting CBC as a better alternative. The theory was that CBC should provide substantial gains in accuracy, since choices are more natural. In reality it failed to deliver clear repeatable gains; while adding complexity and losses in functionality.

With the benefit of hindsight it clear that metric conjoint analysis is a better all-rounder in practice. It can be used on its own, or if larger attribute sets are required, hybridized by bridging partworths with partworths from a self-explicated exercise.

Metric conjoint analysis is more cost effective

Metric conjoint analysis parameters can be estimated for a single individual. You scale the sample size to represent a population more accurately, not for the sake of parameter estimation. In contrast, CBC requires a much larger sample (usually 300+) just to be able to estimate parameters, since choices provide less information than ratings. You know which option is most preferred, but you have no data on the degree of preference of each option not chosen.

In fact CBC, and its various flavours, do not estimate individual level parameters directly. The simplest form of CBC only provides one set of parameters for the entire sample. To ‘estimate’ individual-level parameters, or at least come close to it, information is 'borrowed' from the global or latent class parameters to estimate individual parameters and then an assumption is made regarding the distribution form of these parameters across individual respondents. For example hierarchical bayes assumes a multivariate normal distribution across individuals. As to whether an individual really has those parameters, is not always certain since insufficient data is collected at the individual level.

Works better on small screens

Metric conjoint analysis isn't hampered by smaller screens. CBC conjoint is burdened with the requirement that at least two alternatives (usually more) are shown next to each other on a screen. Fitting an entire 'choice set' on screen – in a legible way - is often impossible. As many respondents now choose to complete surveys on smartphones, rather than desktops or laptops, this isn’t a trivial concern. While respondents could conceivably scroll horizontally to view all of the options, this is inconvenient and risks respondents not seeing all of the options.  Metric conjoint analysis, with its 'one at a time' (sequential monadic) approach doesn't have this problem. Each profile usually fits comfortably on screen, and even if scrolling is required, it is normally vertically; a process necessary to find the rating scale and button to 'continue' at the bottom, making it unlikely they will miss any aspect of the profile.

Metric conjoint analysis places less cognitive load on survey respondents

Metric conjoint analysis requires less effort on the respondent's part, since respondents only need to rate one profile at a time. In contrast, CBC conjoint requires respondents to read through multiple profiles in each choice set before making a decision. I have seen some run as large as eight profiles across – a large cognitive load, for very little yielded in terms of information gained (i.e. a single choice).

An example from the cosmetics market is shown below. A CBC layout is shown on the left, while a metric conjoint analysis profile is shown right. For example a respondent might choose option 3 with levels - Este Lauder, made in Switzerland, SPF 30 - and so on. But to do that they must first have read the other profiles. In the metric conjoint example, a single profile is shown at a time in random order and a rating is collected.

Figure 1: CBC vs metric conjoint analysis layout


In fact, across all choice sets in a questionnaire - more profiles are required for a given number of attributes and levels. This increases total exercise load, which likely reduces data quality.

Less complex and easier to communicate

CBC conjoint (also referred to as discrete choice modelling) is a blanket term that conceals a bewildering array of options, and things can get complicated very quickly. Not only are there numerous models (such as Hierarchical Bayes and Latent Class) and software packages to choose from, there are numerous decisions you must make prior to launch and after the study completes. These include decisions regarding the sample design, survey mode, experimental design, parameter estimation, partial profiles, hybridization and so on. Each of these can take considerable design time, and I haven't even gotten to issues regarding the simulator setup, which is an entire topic on its own.

So CBC can become enormously involved for the practitioner. Worse, research users are going to have a harder time grasping the end result.

Let's take the parameters as an example. Metric part-worths are easy to explain as simple deviations from the average. In contrast, the parameters of CBC are expressed in terms of log odds, which even when exponentiated and expressed as odds ratios is still confusing.
So unless you can be certain that there will be very substantial gains in accuracy for your project, CBC and its various flavours don’t seem to be worth the trouble.

Monadic exposure is more realistic than choice sets in certain industries

It's often been claimed that CBC is somehow more 'realistic'. While the choice sets of CBC might seem ideal in the world of FMCG, there are numerous industries where you are unlikely to have an array of competitors standing right in front of you at the moment of choice.

Many real world choice situations are more realistically measured in a sequential monadic way. Examples include online stores, universities, cars, banks, insurance, software and housing.
Irrespective, it seems that both classes of conjoint still work in practice, even when the data collection approach doesn’t mimic reality in this one aspect.

No IIA issue and no ratio scaling issue

IIA
IIA is an issue with CBC, that gives incorrect share estimates, especially for similar or substitute products in simulations. It was never an issue for the most common decision rule in metric conjoint analysis - maximum utility - nor for randomized first choice (RFC) or RFC Bolse. It was however an issue with the BTL decision rule, but newer improvements allow for differential substitution, which eliminates the need for an IIA assumption. Metrisim, will implement this modified form of BTL as an option in addition to traditional BTL in the near future. In terms of newer forms of CBC, there are claims that a mixed multinomial logit could reduce the impact of the IIA issue, but it does not seem clear how this might work in practice.

Ratio scaling
One of the early contentions of the promoters of CBC was that asking for choices provided 'ratio scaled' data – while metric conjoint analysis was limited to the interval scale if ratings were collected (or ordinal if rankings were collected). This isn’t true, since metric conjoint analysis adds another processing stage called ‘decision rules’ (such as Max Utility or BTL) which produce ratio scaled data – share of choices or volume.  

Comparable performance

While certain software developers have claimed - since at least the 90s - that CBC should be more accurate than metric conjoint analysis and other traditional conjoint analysis methods, this hasn’t proven true.  It seems the claim relies on theory rather than empirical data. The chain of logic usually goes “choices are more realistic / natural and therefore the resulting model that is estimated using those choices as input must somehow be more accurate”. However, this ignores the fact that conjoint analysis has multiple stages – not just data collection – and the other stages had to be altered in ways that were - in many ways - a step backward.

Real world results haven’t supported the claims of greater accuracy; both in terms of parameter estimates and in terms of predictive validity.

Note: below I refer to metric conjoint analysis as RB (ratings-based conjoint analysis) as this tends to be the preference in the academic literature.

In terms of parameters, Karniouchina et al. (2008) found only slight differences between parameter estimates – implying similar estimates of attribute importance. Indeed Karniouchina et al. (2008) concluded "This study, along with the other articles in this research stream, strongly suggests that in traditional conjoint tasks, the parameter estimates produced by RB (metric) and CB conjoint models are likely to be quite similar."

In terms of predictive validity, a study by Elrod et. al (1992) of rental apartments demonstrated that RB (metric) and CBC conjoint produced similar results, "both approaches predict holdout shares well…".

Karniouchina et al. (2008) in a study of laptops found that 'hit rates' (percentage of times the hold-out choice matches predicted choice) at the individual level were better for a more complex form of CBC called hierarchical bayes (HB CBC); but no significant difference was found with segment level hit rates or aggregate level hit rates. In terms of predicted share of choice "no significant differences between the individual- or segment-level RB (metric) and CB models " were found, while there was a significant difference at the aggregate level. A peculiarity of this study should be pointed out, in that HB was used for the individual level parameter estimates for metric conjoint analysis.

Vriens and Oppewal (1998) showed that individual level RB (metric) – individual level is the standard approach - outperformed CBC in some situations and CBC outperformed in others – dependent on choice set size. To get RB (metric) to underperform consistently, the authors had to dumb the RB (metric) down by aggregating the parameters at a latent class level.

Natter and Feurstein’s (2001) study calls into question claims that HB and latent class are solutions to resolve CBC’s major shortcoming; namely the lack of sufficient information provided by choices to estimate parameters at the individual level. The authors compare these models to real world scanner data. Their research “...demonstrates that, in contrast to the performance using hold-out tasks, the real world performance of Hierarchical Bayes and latent class is similar to the performance of the aggregate model...”.

Lastly, even though this last reference is not to empirically supported theory, it is of interest to mention that Guyon and Petiot (2011) point out that in markets where a large amount of heterogeneity is expected, RB (metric) is likely the better option. I’m inclined to agree with this based on HB’s normality assumption for the distribution of parameters across individuals.

While hardly an exhaustive examination of academic studies on this topic, these few studies should make it clear that there is nowhere near a consensus on CBC being superior in predicting hold outs (preference share at the aggregate level). If the aim of your study is to predict market share, rather than preference share, then any differences in performance are even less relevant once external effects such as distribution are incorporated.

References

Baier, Daniel & Pełka, Marcin & Rybicka, Aneta & Schreiber, Stefanie. (2015). Ratings-/Rankings-Based Versus Choice-Based Conjoint Analysis for Predicting Choices. 10.1007/978-3-662-44983-7_18.

Elrod, T., Louviere, J. J., & Davey, K. S. (1992). An Empirical Comparison of Ratings-Based and Choice-Based Conjoint Models. Journal of Marketing Research, 29(3), 368. doi:10.2307/3172746

Guyon, H. & Petiot, J. (2011). Market Share Predictions: A New Model with Rating-Based Conjoint Analysis. International Journal of Marketing Research, 53(6), 831–857. https://doi.org/10.2501/IJMR-53-6-831-857

Karniouchina, Ekaterina & Moore, William & Rhee, Bo & Verma, Rohit. (2009). Issues in the Use of Ratings-Based Versus Choice-Based Conjoint Analysis in Operations Management Research. European Journal of Operational Research. 197. 340-348. 10.1016/j.ejor.2008.05.029.

Natter, M., & Feurstein, M. (2001). Correcting for CBC model bias. A hybrid scanner data - conjoint model. (June 2001 ed.) SFB Adaptive Information Systems and Modelling in Economics and Management Science, WU Vienna University of Economics and Business. Report Series SFB "Adaptive Information Systems and Modelling in Economics and Management Science" No. 57 https://doi.org/10.57938/646d549e-659b-45bb-b450-e6736f3af62f

Vriens, M., Oppewal, H., & Wedel, M. (1998). Ratings-Based versus Choice-Based Latent Class Conjoint Models. Market Research Society. Journal., 40(3), 1-11. https://doi.org/10.1177/147078539804000304 (Original work published 1998)




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