How to interpret significance of interaction term?

Question

I have a problem interpreting an interaction effect. The interaction term (continuous_variable*Female) is significant (p < .05) in logistic regression, but the simple slope analysis suggests that the slopes of the continuous_variable (as a predictor) is not significant for Female=1 or Female=0

> interactions::sim_slopes(my.logit, pred = continuous_variable, modx= FEMALE, johnson_neyman = FALSE)
    SIMPLE SLOPES ANALYSIS 

    Slope of continuous_variable when FEMALE = 0.00 (0): 

       Est.   S.E.   z val.      p
    ------- ------ -------- ------
      -0.10   0.07    -1.34   0.18

    Slope of continuous_variable when FEMALE = 1.00 (1): 

      Est.   S.E.   z val.      p
    ------ ------ -------- ------
      0.10   0.09     1.17   0.24

However, when when I take continuous_variable as a moderator, simple slope analysis suggest significant slopes as below:

> interactions::sim_slopes(my.logit, pred =FEMALE , modx= continuous_variable,johnson_neyman = FALSE, robust='HC1')
        SIMPLE SLOPES ANALYSIS 

        Slope of FEMALE when continuous_variable = 0.06 (- 1 SD): 

          Est.   S.E.   z val.      p
        ------ ------ -------- ------
          0.10   0.14     0.75   0.45

        Slope of FEMALE when continuous_variable = 0.88 (Mean): 

          Est.   S.E.   z val.      p
        ------ ------ -------- ------
          0.27   0.10     2.70   0.01

        Slope of FEMALE when continuous_variable = 1.71 (+ 1 SD): 

          Est.   S.E.   z val.      p
        ------ ------ -------- ------
          0.43   0.13     3.22   0.00

Not sure how to interpret the significance of interaction term along with these simple slope analyses results. Does it suggest that I failed to find support for the interaction?

Answer 1

The significant interaction indicates that there is evidence that the simple slope of continuous_variable when FEMALE = 0 is different from the simple slope of continuous_variable when FEMALE = 1. Considering your first table, this means that -.10 is statistically significantly different from .10. It says nothing about whether each simple slope differs from zero.

You may wonder why, if you don't have evidence that either simple slope is different from zero, you can say the slopes are different from each other. Nonsignificant simple slopes don't tell you that the population simple slope is equal to zero; it just says you don't have enough precision to determine whether each population slope differs from zero. It's possible that one of the population slopes is zero and the other isn't, or they both are different from zero. Your results indicate that they are not both zero (because you have evidence they differ from each other), but that's all you know.