Hi Everyone,
I am working with data of SNPs, I want to do logistic regression analysis.
In multinomial logistic regression, is it compulsory to choose most common genotype as reference? or I can choose any genotype as reference?
In my one SNP (Genotypes: II, ID, DD), when I choose most common II genotype as reference than Odds ratio come out like 0.57, but on choosing ID genotype Odds ratio change to 1.67 with p
That seems strange, but it may nevertheless be possible. Look at your numbers - what per cent of carriers of each genotype have the disease?
If there is a similar chance of having the disease amongst the 'II' and 'DD' genotypes, but vastly different among carriers of the 'ID' genotype, it means your calculations are correct and it is certainly an interesting result. This is referred to as 'heterozygote advantage (or disadvantage)' - several such cases have already been described (see link).
https://en.wikipedia.org/wiki/Heterozygote_advantage#In_human_genetics
The regression does not care what reference you chose. You can chose what you want, and it is always your responsibitity to interpret the coefficients correcty, anyway.
The "category" you choose as reference will determine the manner in which you infer your results. Therefore, it is case dependent. In my area of research, severe injuries are often selected as the "base case". These are also the least occurring, in terms of injury severity. As long as you are calculating your "base case" constant and coefficients correctly, you are just fine.
There is no any restriction for choosing your reference category. You can select any one out off three as your reference category.
But just keep in mind while interpretating your results that you will interpret the results according to your refrence category.
A reference category in binary logistic or logistic regression is used to compare one situation to another in a covariate against dependent variable. For example, if you have Gender, male or female as 1 and 2 (scores), respectively, and you are going to regress against some dependent variable e.g., some practices etc.; if you select first as reference, the tool will opt males as reference against females to regress it with practices.
Malik Olatunde Oduoye , it requires some level of abstraction to wrap your head around.
Consider this simple case: you have two groups in which you measured the value of some variable. Say you measured the weight of sample of male and of female bugs. You are interested to analyze the expected (mean) difference between the weights of males and females.
A statistical model tries to express the expected (mean) weight as a function of sex.
Now "sex" is a binary (categorical, nominal) variable. How to use this in a mathematical formula that operates on numbers? This is where we need to encode the different possible values of the variable "sex" by different values of a numerical variable that we can use in a formula.
There are no restrictions in how to encode names/groups/categories by numbers. However, some ways will give you results that are meaningful for your research question and that you can readily interpret. We will now first take a small detour to demonstrate this, before coming to the "usual solution".
You have two sexes, and you may think of using an indicator function for each of the sexes that take the values 1 or 0, depending on whether the sex is male or female. These indicator variables can be used to multiply the expected weights of the respective sex, and these products can be added to give the expected weight of the desired sex.
This is the mapping from sex to the values 0 or 1 based on two separate indicator functions:
Imale(sex) = {if sex = "male" then 1, otherwise 0}
Ifemale(sex) = {if sex = "female" then 1, otherwise 0}
The function of the expected value is then
µ(sex)= bmale*Imale(sex) + bfemale*Ifemale(sex)
Hence, µ(male) gives bmale*1 + bfemale*0 = bmale and µ(female) gives bmale*0 + bfemale*1 = bfemale
Although this function works, it is somewhat unwieldy. It is about two coefficients, bmale and bfemale, and a statistical model based on this function can estimate their values along with standard errors, confidence intervals, and p-values, if you wish. The problem with this formula is that it does not give you direct access to what you actually wanted to investigate: the difference between males and females.
There is, of course, a more convenient function to address this directly. This function needs only one indicator variable for one of the sexes and includes an intercept term that will represent the expected value of the other sex. You are free to chose which sex should be represented by the intercept term. This is the "reference". Let's say you decide using females as the reference, then the intercept is bfemale and indicator function would be Imale which is multiplied with a coefficient d which will then represent the mean difference between females and males:
µ(sex)= bfemale + d*Imale(sex)
Here, µ(female) gives bfemale+d*0 = bfemale and µ(male) gives bfemale + d*1 = bfemale+d, so
µ(male) - µ(female) = d
As is obvious here, the coefficient d represents the difference in the mean weight between males and females, and a statistical model will provide an estimate for this difference with corresponding standard error, confidence interval, and p-value.
Of course you can choose to let the intercept represent the mean weight of males as well. The indicator function must then be Ifemale and the coefficient d then represents the difference in the mean weight between females and males. You may convince yourself by actually calculating the results of the formula for the two possible sexes:
µ(female) gives bmale+d*1 = bmale + d and µ(male) gives bmale + d*0 = bmale, so µ(female) - µ(male) = d
This is it. Practically, statistical software will automatically encode categorical variables into so-called dummy variable by applying the respective indicator functions and use these dummy variables in the statistical models. But these are technicalities.
This interpretation of the coefficient d depends on what sex you have chosen as the reference. If you have chosen males as reference and d > 0, then female bugs are expected to be heavier than male bugs. If you have chosen females as reference and d > 0, then female bugs are expected to be lighter than male bugs.
- Badges
- Science topic
- Similar topics
- Correction