4

Is there an interaction effect, or not? Barely. There is an interaction in these data, because the estimate for the interaction coefficient is -0.16 and this seems to be meaningful in the context of the model, given that the estimated coefficient for x is 0.48, although with an intercept of 89 (and the mean of y of 144) it may not be meaningful in the ...


3

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 ...


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