Equation notation logistic regression

[Luciana Brondi]

Dear colleagues,
For my thesis, I would like to write an equation showing the final Model for a binomial logistic regression analysis I constructed using a complex survey. The outcome/dependent variable is DiarrCost, a binary variable. I used svy command throughout the analysis and all the independent variables are categorical. There is an interaction term (HFocusSt*Wealth). Does the equation notation underneath look right to you? Does it change if I use logistic or logit (in terms of equation notation).

Stata command:

svy: logit DiarrCost Sex Infant Wealth MotherEd HFocusSt HFocusSt _Wealth

Proposed equation notation:

Logit (DiarrCost) = a + b(Sex) + b(Infant) + b(Wealth) + b(MotherEd) + b(HFocusSt) + b(HighFocusSt* Wealth) + e

[Maarten Buis]

Almost, but not quite. What you are modeling is not diarrcost, but the probability that diarcost equals 1. As a consequence there is no error term.

\(
\mathrm{logit}(\mathrm{Pr}(DiarrCost=1)) = \beta_0 + \beta_1 sex + \beta_2 infant + \beta_3 wealth + \beta_4 mothered + \beta_5 hfocussst + \beta_6 hightfocussst \times wealth
\)


\(
\log(\frac{\mathrm{Pr}(DiarrCost=1)}{1-\mathrm{Pr}(DiarrCost=1)}) = \beta_0 + \beta_1 sex + \beta_2 infant + \beta_3 wealth + \beta_4 mothered + \beta_5 hfocussst + \beta_6 hightfocussst \times wealth
\)

If you want an error term, you could argue that what your are modeling a latent propensity for diarrcost to be 1.

As an aside, you should never make your own interaction terms. Instead you should use Stata's factor variable notation to include interaction terms. See help fvvarlist

[Luciana Brondi]

Hi, Maarten, many thanks. I will use the factor notation to report my table of results, i.e, describe the Odds ratio in each category. To construct the model I used the Purposeful selection of variables as described by Hosmer and Lemeshow (3rd edition-chapter4) and tested for potential interacions.