Regression or Panel model (fixed or random effect)? I have a question that I am sure you can help me with. 
I have data on 100 individuals from an experiment, including a bunch of characteristics for each of these individuals (gender, field of specialty, etc...). 
These individuals were during the experiment subjected to two successive and different treatments, in random order. A dependant continuous variable (risk-taking) was measured for each treatment. I therefore have two measures of this dependent variable per participant, one for each treatment. I am interested both in the effect of the treatment and the effect of the individual characteristics (gender, field of specialty, etc..) on risk-taking. See scheme below (with ID the identifying number of the individual). 

I have started to analyze the data by using a classic OLS regression. Should I rather use some form of panel model/repeated measure model (with fixed, random or mixed effect?) to take into account the fact that I have two measures per individual? I am unfamiliar with those models. 
Thank you very much in advance!
 A: I know this is an old question but I am adding an answer to get feeback.
This is a crossover study of 2 treatments and data can be reorganized as follows variables (columns):
ID gender specialty order risk0 risk1 diffrisk

Where risk0 and risk1 are risk values for 2 types of treatments and diffrisk is difference between the two. Order is treatment order (0-1 or 1-0).
To determine if 2 treatments have different effects, one can simply use paired Student t-test to compare risk0 and risk1.
To determine influence of other factors, one can use diffrisk. Analysis can be done using regression as:
diffrisk ~ gender + speciality + order

Or, one can use mixed effects model (with data in original form) in following manner:
lmer(risk ~ Treatment + gender + specialty + order + (1|ID), mydata)

hence, keeping ID as a random effect.
The order is commonly ignored for analysis and not kept in equation.
A: There are multiple methods to analyze this but I think it is important to first think about the underlying design. One way to conceptualize this design is as a 2 by 2 factorial. Within this framework, you have two treatments (coded as 0 and 1 in your above dataset) and two orders of presenting this treatment (treatment order 0-1 and treatment order 1-0). You don't currently have a variable for order but I'm assuming you can recover this information and add it to the dataset. Even if you are not explicitly interested in the order, it is part of the design that generated these data and as such should be included in the statistical model. Any analysis method also needs to take into account that individuals get both treatments (treatment is a "within groups" factor or repeated measure). You could use either regression methods or ANOVA methods (which are really the same thing but different output). You would have a main effect for treatment and for order. You could also test for an interaction between treatment and order (I'm assuming that your data is balanced -- you have equal numbers in each order). If so, testing the interaction is uncomplicated as it is orthogonal to the main effects. If your design is unbalanced, you need to be more careful in testing the interaction (there is a literature on this).
