Dummy or effects coding

[sab]

Hello,

For the DCE I am designing I am interested in whether 2 new types of health test will influence uptake compared to 2 tests that are currently used. The current tests are based in hospital but the new tests could be done in community settings. I will therefore have the following attributes:

type of test attribute (4 levels)
- current test 1
- current test 2
- new test 1
- new test 2

location
- hospital
- community setting 1
- community setting 2

It will be a single profile design where people will be shown a single profile and asked whether they would have the test or not (to reflect a realistic choice for patients).

I've been under the impression that it is better to use effects coding as dummy coding can lead to misinterpretation of the estimates - the base level will be implicitly equal to zero and there is no unique interpretation of B0.(Bech & Gryd-Hansen, 2005). I have read Daly et al., 2016 paper on dummy coding vs effects coding, but what I still don't understand is if I use effects coding how I would answer my key research questions which require me to examine uptake differences between current practice and hypothetical future practice, as below:

Type of test:
Current test 1 and new test 1
Current test 1 and new test 2
Current test 2 and new test 1
Current test 2 and new test 2

Location:
Hospital and community setting 1
Hospital and community setting 2
Community setting 1 and community setting 2

I'm new to DCEs so want to make sure I understand how I will interpret the analysis in advance.

[Michiel Bliemer]

Both dummy and effects coding can be used to test your hypotheses.

If you use effects coding and choose the first level as the base level (but you can select any other level as base level), then you would estimate parameters b1, ..., b5 in the model.

type of test attribute (4 levels)
- current test 1 (base = -b1-b2-b3)
- current test 2 (b1)
- new test 1 (b2)
- new test 2 (b3)

location
- hospital (base = -b4-b5)
- community setting 1 (b4)
- community setting 2 (b5)

Based on parameter estimates for b1, ..., b5 and their covariance matrix, you can use the Delta method to conduct the following statistical tests:

Type of test:
Current test 1 and new test 1: H0: -b1-b2-b3 = b2 --> H0: -b1-2*b2-b3 = 0
Current test 1 and new test 2: H0: -b1-b2-b3 = b3 --> H0: -b1-b2-2*b3 = 0
Current test 2 and new test 1: H0: b1 = b2 --> H0: b1-b2 = 0
Current test 2 and new test 2: H0: b1 = b3 --> H0: b1-b3 = 0

Location:
Hospital and community setting 1: H0: -b4-b5 = b4 --> H0: -2*b4-b5 = 0
Hospital and community setting 2: H0: -b4-b5 = b5 --> H0: -b4-2*b5 = 0
Community setting 1 and community setting 2: H0: b4 = b5 --> H0: b4-b5 = 0

If you use dummy coding you could do exactly the same tests but it would be (much) simpler:

type of test attribute (4 levels)
- current test 1 (base = 0)
- current test 2 (b1)
- new test 1 (b2)
- new test 2 (b3)

location
- hospital (base = 0)
- community setting 1 (b4)
- community setting 2 (b5)

Type of test:
Current test 1 and new test 1: H0: 0 = b2 --> H0: b2 = 0
Current test 1 and new test 2: H0: 0 = b3 --> H0: b3 = 0
Current test 2 and new test 1: H0: b1 = b2 --> H0: b1-b2 = 0
Current test 2 and new test 2: H0: b1 = b3 --> H0: b1-b3 = 0

Location:
Hospital and community setting 1: H0: b4 = 0
Hospital and community setting 2: H0: b5 = 0
Community setting 1 and community setting 2: H0: b4-b5 = 0


Michiel

[sab]

Thanks very much Michiel! Is it personal preference then as to whether dummy or effects coding is used?

[Michiel Bliemer]

Yes mostly personal preference.

[sab]

Hi there,

I have a follow up question to the above post.

I proceeded with the effects coded design and I'm analysing the data using a mixed effects logistic regression. When I test whether there is a significant difference between two levels of an effects coded variable (e.g. I am using the lincom command in Stata to compare the coefficient for current test to the coefficient for new test), I get significant results, but the predicted probabilities for these two variables have overlapping 95% CIs - is this unusual? Moreover, when I ran the model using dummy coding to explore this further, the dummy coded coefficient representing the difference between the two levels (e.g. for new test when current test is used as the base level) is non-significant, when my expectation was that this should give the same result as the lincom test I used.

My understanding is that the lincom test accounts for the covariance of coefficients, but I am confused as to whether it is appropriate to report these tests given that they seem at odds to visual inspection of the predicted probabilities and the dummy coded model output.

Thanks very much in advance for any advice you can offer.

[Michiel Bliemer]

Comparing levels across dummy and effects coding should give the same results since the same difference in levels of utility between the two levels is tested, it should give the same result. I am not familiar with Stata so I am not sure what it use.

Yes if you look at confidence intervals only, then testing for statistical difference will not account for covariances, whereas a proper statistical test would use the Delta method to calculate the standard error of the difference of two parameters, which does account for covariances. Therefore, the correct statistical test uses the Delta method, overlap in confidence intervals is not an accurate statistical test for comparing parameter values.

Michiel

[sab]

Thanks very much!