# Binary response variable with ordinal, discrete and continuous covariates

Let consider a study to know the factors influencing adoption of a new technology. A total of eighty farmers were selected randomly ($40$ adopted the technology and $40$ did not). The data file contains eight variables [Adoption ($1$ = adopted and $0$ = not adopted), age, education, land_size, working_members, farming_experience, risk_orientation]. Analyze the data and draw your conclusions. Data is given below.

$$\begin{array}{|c|c|c|c|} \hline \text{Adoption} &\text{age}&\text{education} &\text{land_size}&\text{working_members}&\text{farming_experience}&\text{risk_orientation}\\ \hline 1 &40 &10 & 3.5 & 6 &20& 30\\ \hline 1 &58 &8 &5 &5 &40 &31\\ \hline 1 &40 &12 &2 &8 &20 &33\\ \hline 1 &49 &12 &4 &6 &30 &32\\ \hline 1 &42 &12 &5 &4 &25 &35\\ \hline 1 &55 &15 &3 &4 &40 &31\\ \hline 1 &49 &12 &6 &4 &30 &34\\ \hline 1 &45 &5 &3 &5 &30 &36\\ \hline 1 &40 &10 &4 &5 &25 &31\\ \hline 1 &38 &9 &5 &7 &20 &34\\ \hline 1 &42 &8 &2.5 &4 &30 &28\\ \hline 1 &39 &10 &2.5 &5 &15 &36\\ \hline 1 &44 &12 &2 &6 &25 &31\\ \hline 1 &45 &15 &4 &5 &25 &32\\ \hline 1 &49 &10 &4 &4 &30 &33\\ \hline 1 &42 &8 &3.5 &6 &25 &33\\ \hline 1 &42 &10 &4.5 &5 &20 &34\\ \hline 1 &55 &12 &5 &6 &35 &32\\ \hline 1 &45 &10 &4 &6 &30 &33\\ \hline 1 &38 &10 &3 &7 &20 &35\\ \hline 1 &46 &15 &5 &6 &25 &33\\ \hline 1 &51 &12 &4 &6 &30 &34\\ \hline 1 &43 &12 &2.5 &5 &30 &31\\ \hline 1 &50 &8 &1.5 &5 &25 &35\\ \hline 1 &46 &10 &3 &5 &30 &33\\ \hline 1 &53 &4 &3.5 &5 &35 &34\\ \hline 1 &48 &10 &3 &6 &30 &33\\ \hline 1 &55 &15 &2.5 &6 &40 &33\\ \hline 1 &37 &10 &2.5 &6 &20 &34\\ \hline 1 &49 &8 &3 &5 &30 &30\\ \hline 1 &40 &10 &4 &5 &25 &33\\ \hline 1 &38 &12 &2 &5 &20 &31\\ \hline 1 &41 &12 &3 &5 &25 &33\\ \hline 1 &40 &10 &1.5 &6 &25 &33\\ \hline 1 &52 &15 &2 &6 &30 &33\\ \hline 1 &36 &10 &2 &5 &21 &31\\ \hline 1 &54 &15 &2 &5 &39 &34\\ \hline 1 &42 &10 &3 &6 &27 &34\\ \hline 1 &38 &12 &2 &6 &25 &33\\ \hline 1 &50 &5 &2 &5 &35 &33\\ \hline 0 &45 &8 &4 &6 &30 &23\\ \hline 0 &48 &10 &3 &7 &30 &26\\ \hline 0 &55 &4 &2.5 &7 &20 &31\\ \hline 0 &59 &8 &1.5 &5 &40 &28\\ \hline 0 &54 &4 &3 &6 &40 &32\\ \hline 0 &50 &8 &2 &5 &30 &26\\ \hline 0 &49 &8 &5.5 &5 &20 &29\\ \hline 0 &58 &10 &3 &7 &30 &33\\ \hline 0 &40 &8 &3 &4 &20 &27\\ \hline 0 &52 &4 &4 &4 &40 &33\\ \hline 0 &56 &10 &3 &5 &30 &26\\ \hline 0 &49 &4 &1 &4 &30 &33\\ \hline 0 &44 &12 &3.5 &5 &30 &27\\ \hline 0 &52 &9 &2 &5 &40 &29\\ \hline 0 &45 &10 &2 &7 &30 &30\\ \hline 0 &42 &5 &3 &5 &20 &26\\ \hline 0 &42 &15 &3 &6 &30 &34\\ \hline 0 &48 &12 &3 &5 &35 &29\\ \hline 0 &52 &8 &3 &4 &30 &33\\ \hline 0 &60 &10 &3 &5 &40 &34\\ \hline 0 &49 &4 &3.5 &4 &30 &29\\ \hline 0 &60 &7 &4 &6 &15 &33\\ \hline 0 &58 &10 &2 &6 &38 &30\\ \hline 0 &40 &5 &2.5 &3 &25 &33\\ \hline 0 &49 &8 &2 &5 &30 &30\\ \hline 0 &42 &4 &3.5 &5 &25 &34\\ \hline 0 &55 &5 &1.5 &6 &20 &31\\ \hline 0 &55 &7 &1.5 &5 &40 &30\\ \hline 0 &48 &4 &3 &5 &30 &34\\ \hline 0 &49 &12 &3 &5 &25 &30\\ \hline 0 &52 &10 &2.5 &4 &30 &33\\ \hline 0 &45 &15 &2 &6 &25 &31\\ \hline 0 &51 &7 &3 &5 &40 &33\\ \hline 0 &40 &8 &2.5 &6 &22 &34\\ \hline 0 &55 &5 &2.5 &6 &30 &33\\ \hline 0 &51 &10 &3 &6 &30 &30\\ \hline 0 &44 &5 &3 &5 &25 &34\\ \hline 0 &55 &10 &1.5 &5 &40 &34\\ \hline 0 &51 &7 &1 &5 &30 &36\\ \hline 0 &50 &4 &1.25 &5 &40 &28\\\hline \end{array}$$ Trial: I am interested to test the hypothesis $H_0$ : There is no significant effect of these characteristics on the adoption of the technology. For that purpose I think I should use Binary logistic regression. But education is ordinal variable, working members is discrete variable and others are continuous variable. So am I analyzing correct or not? What can I do more with the data. Any help will be highly appreciateable.

## 1 Answer

As you are interested in explaining the effect of the other variables upon the adoption of technology, you can consider Adoption as your response variable, and the remaining covariates as explanatory variables.

Your response variable is binary, meaning that you will have binomial errors. It is thus sensible to use logistic regression. There is a lot of information on how to perform this and interpret the results:

https://stats.stackexchange.com/a/279899/139031 (This also explains variable definitions)

You can then consider significance for each variable using an analysis of deviance or likelihood ratio tests if you are comparing nested models:

https://onlinecourses.science.psu.edu/stat504/node/157

And for an excellent answer on how ordinal variables are interpreted in logistic regression, see:

https://stats.stackexchange.com/a/60821/139031

At a push, the discrete variable "working members" could be treated as a continuous variable given the range, but in short the type of explanatory variables is usually more important for interpretation than for model selection.

Note: There may be issues in assuming the sample is random, given you have an equal proportion of cases and controls (Adoption=1, Adoption=0). Selection bias may be an issue unless it happened purely by chance.

I hope that helps :)