Can I use logistic regression when my IV is dichotomous but my DV is continuous? I have a longitudinal data set in which my predictor/Independent Variable is dichotomous and was assessed at age 4 years, and my outcome/Dependent Variable (depressive symptoms) was assessed at 16 years.  I would rather not arbitrarily dichotomize the DV, and I would prefer to avoid non-parametric stats so that I could include some covariates.
Naively, I would think that one could use a dichotomous IV but continuous DV in logistic regression, though I would assume that technically I would be using depressive symptoms to predict my IV?  Is there any precedence for this in the literature (or alternative analyses to consider)?
Thanks. 
 A: If your dependent variable is continuous, logistic regression isn't appropriate.  In general, the domain of your predictors isn't relevant to the choice of model family.  It's the domain of the dependent variable.
I got confused with this too when I was first learning about regression models.
A: I am assuming that you realize logistic regression is only suitable for binary outcome. What I think you're asking is if you can flip the identify of a binary IV and a continuous DV, and fit them into the outcome and exposure of a logistic model accordingly.
The answer is probably not. Because regression model assumes the independent variables are measured without error. If you swap their identity, you would attribute the residual to the exposure, and worse, you're assuming the current depressive symptom score is measured without error.
Try to use model closer to linear regression, and put them IV and DV in their right spots as best as you can.
A: The usual statistical method for relating a continuous (and hopefully normal) outcome to a categorical explanatory variable is ANOVA. In the case of a binary IV, this is equivalent to doing a two-sample t-test.
In this case, start by doing a box-and-whisker plot of your depression measure against the two groups of subjects (0 at 4 years old vs 1 at 4 years old). Take a look to see if the conditions for a two-sample t-test are there, and if so, do the test. Otherwise, you could do a non-parametric test (Mann-Whitney, for example).
A: I agree with the other posts. You cannot utilise logistic regression when your dependent variable is continuous. Your dependent variable definitely needs to be a categorical (i.e. a 0-1) variable in order to utilise logistic regression in the way this statistical approach is intended. Specifically, logistic regression is designed to predict the probability that a particular scenario or outcome will occur, i.e. it is designed to ask questions like: "What is the probability of a consumer purchase?" (purchase versus no purchase) or "What is the probability that a merger will be approved by the shareholders?" (approval versus withdrawal) ... and so forth. As some of the other posts point out, you will probably want to go ahead with a one-way analysis of variance (ANOVA). But you can easily use multiple regression as well if you're more comfortortable with this approach. To many people, regression is easier to understand than ANOVA, and it is also perfectly possible to perform a categorical analysis with the regression (I assume this is what you're interested in). However, the choice will also, in part, depend on the typical approach to a research question of your type. For example, within my field of expertise (finance), ANOVA is a very rare thing, so the reader is probably going to be uncomfortable with an ANOVA. So you should definitely also consider who is going to read your article/report/etc. 
