# What is a good model for conditional data?

I am looking for statistical models of conditional data where some variables take certain values conditioned on values of other variables. For example, if $$[x_1, x_2]$$ are two variables defining a phenomenon, and the range of $$x_2$$ is defined based on the selected value of $$x_1$$. For concrete example, if $$x_1 = 2$$, then $$x_2 \in [5, 10]$$ and if $$x_1 = 3$$, then $$x_2 \in [2, 4]$$. How can I model such situation where values possible for $$x_2$$ is dependent on the value of $$x_1$$?

• Are you looking to model parameters of the distribution of $x_{2}$ based on values of $x_{1}$? It appears that both mean and variance of $x_{2}$ in your example vary by value of $x_{1}$ (you have heteroscedasticity). There is something called Double Generalized Linear Models (DGLM) that extend GLM to where mean and dispersion parameters are modeled jointly in terms of covariates after transformation by a link function. – AlexK May 15 at 1:15
• I am looking to model the distribution over $x_2$ and $x_1$ together. Thank you for the pointers. I will look at them. – randomprime May 15 at 1:18
• What is $x_3$ in your description? – user158565 May 15 at 4:13
• @user158565 sorry fixed the typo. It is $x_2$. – randomprime May 15 at 4:32