How to interpret the significance of estimates if it differs between regression models? [duplicate]

Question

I am trying to analyse the impact of experiencing a certain incident on the pro-unification opinion of people. If the incident occurs, they can occur in solely 3 different types: A, B and C. We assume that there is no other type of incident. So the general form of the regression is: 𝑜𝑝𝑖𝑛𝑖𝑜𝑛=𝛼+𝛽∗𝑖𝑛𝑐𝑖𝑑𝑒𝑛𝑡+𝜖 Please note that I left out the subscripts for simplicity reasons.

I have troubles interpreting the coefficients starting from model (4). First, people who experienced incident of type A seem to have a significant effect (*, 10% level) on opinion compared to people with no incident or other types of incident. However, the effect of incident B (model 5) and C (model 6) are not significant at all. However, in model (6) the estimate for incident A is not significant, but for incident B and C. Further, model (8) also leads to a non-significant estimate of incident A. (Note: "Incident" is not the constant but also a dummy variabel for whether an incident occurred regardless of type of incident.)

How can I interpret the results? Is the result inconclusive? The R-Squareds are similar to each other, so one cannot choose between "better" models via R-Squared.

Answer 1

We interpret coefficients as "the change in the outcome that is associated with the variable increasing by 1, holding fixed all other variables".

In (4), if Incidenty Type A switches from 0 to 1 and nothing else changes, this means we are considering an observation that is an incident of type B or C, and it changes to being type A instead of B or C (thus the incident variable doesn't change, but the Incidenty Type A variable changes). The coefficient is interpreted as "Type A incidents have an outcome that is on average 0.15 higher compared to pooled incidents of type B or C" (But I am curious if "0,15" is a typo...).

In (5) "Type B incidents have an outcome that is on average 0.03 higher compared to pooled incidents of type A or C"

In (6) "Type C incidents have an outcome that is on average 0.05 lower compared to pooled incidents of type A or B"

In (7) "Type A incidents have an outcome that is on average 0.03 higher compared to no incident", "Type B incidents have an outcome that is on average 0.02 higher compared to no incident", and "Type C incidents have an outcome that is on average 0.04 lower compared to no incident"

In (8) "Type A incidents have an outcome that is on average 0.03 higher compared to pooling no incident, incidents of type B, and incidents of type C."