Ascertaining GLM link visually On pg. 125 in Agresti's Categorical Data Analysis, it's suggested by a plot of the dependent variable (a count) vs an independent variable (categorized version of continuous width variable) that the relationship between count and width is linear.
It is then said that a Poisson GLM with the identity link may be appropriate. I think you could also use a normal linear model but the idea is to use the assumption that variance increases with mean in the Poisson.
What I started to wonder is if you can look at a graph and decide that the identity link is appropriate, what would a graph that suggests the log link is appropriate look like? Is this visual approach often used, and is it used for the binomial? It would seem hard to do this with multiple independent variables, but I guess you could make a plot for each variable.

If it were obvious that the variance did change with the mean (for example, one group has a very low mean and very low variance, but another group has a high mean and a high variance) that would suggest that the log link should be used.
It would be easy to graphically determine whether the data follow a binomial family/logit link because the response variable will be either 0 or 1 for each individual.
In practice, it is more common to visually assess the residuals of models than the response variables. By plotting the residuals of an identity-linked linear model against the predicted values, you can easily tell if the variance is changing with the mean even with many covariates or continuous covariates.
