You can run a linear model that you estimate using ordinary least squares (OLS) or maximum likelihood drawing from a gaussian/normal distribution.

Yes

No

Can you assume that β (the effect of a unit increase in x) is the same regardless of which of the two outcomes is coded as success (y==1)?

Yes, theoretically only the sign should differ (+ or -)

No. I have a theoretical reason to model a world in which — if I reverse the direction of the coding of y — I'll have a different slope parameter.

Consider a poisson model. Is it overdispersed?

No

Yes

Consider a parametric or non-parametric event history model.

Consider an ordered logistic model. Does it satisfy the paralell lines assumtion?

Yes

No

You're all set!

What describes your situation best?

I have many categories and they are conceptually ordered

I have few categories

Chooser characteristics

Choice characteristics

Both

You want to run a multinomial logit.

You want to run a conditional logit.

Consider a binomial logistic regression. Another alternative is the probit model.

Take a second look at the distribution of your dependent variable. Is your phenomenon either very rare or very common so that your y is skewed (i.e. most of your observations are 0s or 1s) even when you have reasonable variation in x ?

My outcome variable is not exceptionally rare

Yes, I study a rare phenomenon

Consider a complimentary logistic model (aka. the cloglog or the complimentary log-log model).

The comlementary log-log model assumes that predicted probabilities approach 1 at a faster rate than 0. In other words, you find diffferent results depending on which outcome you code as a success (y == 1; usually the rare outcome) and which you code as a non success (y==0; usually the common outcome).

The complementary log-log model is thus different from the more commonly employed logistic and normal (linear) regression. Both the logistic and normal distributions are symmetric. It means they assume that the effect of x is the same regardless of whether a unit increase in x means we approach the 1s or the 0s in the y.

You're all set!

Overdispersion is a symptom of a bad model fit. Consider the sources of this.

My supposedly independent events are correlated

I have excess zeros

I have no idea

You're all set!

Consider a mixed logit.

Positively

Previous events increase the rate of subsequent events.

Other

The data generating process involves a joint probability of two events: One binary and one count process. These two processes can be modeled separately.

• Zero-inflated model
• Hurdle model

• Quasi-poisson
The model alters the standard errors, but not the estimate.
• Negative binomial
The model alters both the standard errors and the estimate by adding an additional parameter.

You can always opt to ignore the information from the ordering and run a multinomial or a binomial logit. In the process, you might also consider merging small categories.

Consider a negative binomial model. The model alters both the standard errors and the estimate by adding an additional parameter accounting for the increasing positive correlation between events.

Are events clustered? Is your model too parsimonious? Additional variables, fixed effects, random effects/hierarchical modeling may help you to find a more stringent fit.