# Tag Info

Interactions in nonlinear models can get very tricky since these models can allow much more heterogeneity/flexibility in response. I always try to leave my linear intuition behind at home when I go out into the wild, nonlinear world, and do some math. So here we go. In a logit with two main effects and an interaction, $$Pr[y = 1 \vert x,z] = \frac{\exp (\... 3 Well the problem is that you are p-hacking like crazy. This kind of multiple testing is the sort of thing that has caused the scientific replication crisis in the social sciences and produced hundreds/thousands of seriously flawed papers. You cant just keep trying different ways of interacting your variables and cutting things up, without destroying the ... 2 When you write: y = \alpha + \beta_1 x_{1} + \beta_2x_{2} + \beta_3x_{3} with your definition of x_{3}, it's the same as y = \alpha + \beta_1 x_{1} + \beta_2x_{2} + \beta_3 x_{1}x_{2} which is the customary form for an interaction term between  x_{1} and x_{2}. In that sense x_3 isn't really "standalone"; you've just effectively used ... 2 It is definitely valid. If theory posits only one interaction, but multiple main effects, then there is no reason to "stuff" the model just to have a kind of symmetry. Note that the model with all interactions would be (much) more complex than one with fewer interactions. As such, I would say that the burden of explanation lies on those who propose ... 2 Original Model The linear regression model you fitted to your data looks like this: dv = \beta_0 + \beta_1conditiontreat + \beta_2age + \beta_3gendermale + \beta_4educationpostgrad + \beta_5educationundergrad + \beta_6conditiontreat:educationpostgrad + \beta_7conditiontreat:educationundergrad + \beta_8conditiontreat:age + \epsilon. The effect of ... 1 The chance of answering correctly decreases significantly by -0.95974 when comparing condition 0 to condition 1 (p < .001) It's Logit(p) rather than p, that decreases significantly by -0.95974 when comparing condition 0 to condition 1, with p being the chance of answering correctly, and:$$ Logit(p) = ln(p/(1-p)) $$cond1:treatment1: When comparing ... 1 Most of the time you should not include the interaction without the main effects. Check out here why. I also found this comment from @Thomas Levine under the same question that might help you: If the interactions are only significant when the main effects are not in the model, it may be that the main effects are significant and the interactions not. ... 1 You have an endogenous variable x_1 which is a factor, let's say that it takes 6 values (x_1 = a",...f"). In your model it enters with an interaction with variables x_2 and x_3. Therefore your model is equivalent to$$y = a_11_{(x_1=a")}x_2+...a_51_{(x_1=f")}x_2+b_11_{(x_1=a")}x_3+...b_51_{(x_1=f")}x_3+cx_4+e$$where 1_{(x_1=a")} = 1 ... 1 Your FE model is$$E[Z_i \vert X_i,Y_i]= a_i + b_1 \cdot X_i + b_2 \cdot Y_i + b_3 \cdot X_i^2 + b_4 \cdot Y_i^2 + b_5 \cdot X_i \cdot Y_i The intercept $b_0$ is not really an ordinary intercept that comes out of the model (since that is eliminated by the demeaning), so I replaced it with the fixed effect $a_i$. You can think $b_0$ as the average value of ...