This note is prepared for those familiar with the specifics of discrete choice experimentation to answer key questions in detail. Please contact the team if you have any further questions about the methodology.

**DCE or conjoint?** Conjoint.ly uses discrete choice experimentation, which is sometimes referred to as choice-based conjoint. DCE is a more robust technique consistent with random utility theory and has been proven to simulate customers’ actual behaviour in the marketplace (Louviere, Flynn & Carson, 2010 cover this topic in detail). However, the output on relative importance of attributes and value by level is aligned to the output from conjoint analysis (partworth analysis).

**Experimental design.** Conjoint.ly uses the attributes and levels you specify to create a (fractional factorial) choice design, optimising balance, overlap, and other characteristics. Our algorithm does not specifically attempt to maximise D-efficiency, but it tends to produce D-efficient designs. It tends to produce designs of resolution IV or V (as such, it does support measurement of two-way interactions, even though they are not used in our modelling at this stage). In most cases, the number of choice sets is excessive for one respondent and the experiment is split into multiple blocks (often between five and ten). We do not support individualised designs (i.e., every respondent has their own block). Each choice set consists of several product construct alternatives and, by default, one “do not buy” alternative. To review the experimental design for your experiment, in your design set-up page, please go to “Advanced options”, then click “Export experimental design”.

**Minimum sample size.** Conjoint.ly automatically recommends a minimum sample size. In most cases, it is between 50 and 300 responses. In our calculations, we use a proprietary formula that takes into account the number of attributes, levels, and other experimental settings.

**Relative importance of attributes and value of levels.** Conjoint.ly estimates a hierarchical bayesian (HB) multinomial logit model of choice using responses deemed valid. The value (partworth) of each level reflects how strongly that level sways the decision to buy the construct. Attributes with large variations in the sway factor are deemed more important. Specifically, we calculate attribute importance and level value scores (partworth utilities) by taking coefficients from the estimated model and linearly transforming them so that:

- in each attribute, the sum of absolute values of positive partworths equals the sum of absolute values of the negative ones, and
- in each attribute, the sum of the spreads (maximum minus minimum) of parthworths equals 100%.

**Marginal willingness to pay.** For experiments where one of the attributes is price, Conjoint.ly estimates a separate model with price as a numerical variable. We also perform checks for appropriateness of calculation of the measure, taking into account both the experimental set-up and the received responses (for example, limiting MWTP calculation in cases where there is non-linearity in price). We use the concept of “Market Value of Attribute Improvement” (MVAI), but unlike in the original paper we do not use the closed-form formula, but rather find the values numerically.

**Share of preference simulation.** Share of preference simulation is performed using individual coefficients from the estimated HB multinomial logit model. Two models for calculating market shares are available:

- “Share of preference” model, which is appropriate for low-risk or frequently purchased products: FMCG, software, etc. This model is applicable in the vast majority of applications.
- “First choice” model, which is suitable for high-risk or seldom purchased products: education, life insurance, pension plans, etc.

**Ranked list of product constructs.** Conjoint.ly forms the complete list of product constructs using all possible combinations of levels and ranks them based on a score computed from the relative level value scores (partworths).

**Segmentation.** Conjoint.ly segments the market based on the individual coefficients from the estimated HB multinomial logit model using k-means clustering. We provide the values of the Calinski-Harabasz criterion (to help choose the appropriate number of clusters) and the Dunn index (to help choose the appropriate number of clusters as well as to decide if segmentation at all is crisp and hence appropriate). We provide the same reporting for each segment.

The raw data collected in all experiments are available in the Excel sheets, which makes it possible to do additional analysis on the data outside of Conjoint.ly. In particular, the “Raw data” sheet will contain the following key tables:

**Raw responses**is the list of all responses (by respondent, question, and block)*participant_id*is the ID of the respondent*block*is the number of the block*set_seq_order*is the question number*alternative_seq_order*is the chosen alternative

**List of levels arranged in questions***alternative_seq_order*is the sequential number of the alternative*AseqNum*is the sequential number of attribute*LseqNum*is the sequential number of the level

The values *set_seq_order* and *alternative_seq_order* are not necessarily in the order in which each respondent sees these, because the rendering of questions is randomised for each respondent, and the rendering of alternatives is randomised for each question.

In cases where you know certain information about your respondents before they enter the survey and want to use that information in your analysis, you can pass the data to Conjoint.ly through the shareable links. For example:

https://run.conjoint.ly/study/970/7txubkovie?customer-id=34324&gender=male

In this example, for this respondent Conjoint.ly will record two GET variables:

- customer-id with the value 34324, and
- gender with the value male.

This information will be available in the Excel export file under the sheet “Raw data”.