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I am currently using the simple slope analysis to examine the significant interaction effects between my continuous moderator and a dichotomous predictor (values 1 & 2)on a continuous DV. I have 2 continuous covariates in the analysis.

My simple slope graph however showed negative values in the DV (i.e: moderator values at predictor value 2 accounted for negative amounts of DV - the slopes crossed the x-axis towards the bottom right direction). Is this possible, or is there some statistical error? I have seen slopes going into the negative values of DV for continuous predictors, but not for dichotomous predictors.

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  • $\begingroup$ What are the units of each of the variables, and the dependent variable in particular? $\endgroup$ – Jeromy Anglim Sep 27 '11 at 4:18
  • $\begingroup$ Hello Jeromy, thanks for the below. The correlations bet the predictors was -0.035 (small) and the range of the DV was 3.00 and values were close to 0. Still working out the unusual results. But here's the units: DV: Range=3.00, Mean=1.41, SD=0.78. Unstandardised coefficients: Predictor(.71), $\endgroup$ – Amaranta Sep 27 '11 at 8:32
  • $\begingroup$ Apologies, here are the figures: DV: Range=3.00, Mean=1.41, SD=0.78. Unstandardised coefficients: Predictor(.71),Constant(3.42), Moderator(-.04), interaction(.04). Variances: predictor(0.02), constant(4.21), moderator(0), interaction(0). Df=92. Moderator: M=86.11, SD=8.92. Hope the above values make sense. $\endgroup$ – Amaranta Sep 27 '11 at 8:44
  • $\begingroup$ Given your range and mean for the DV, a predicted value a little below zero is not surprising. Of course, the more checks you apply, the better. $\endgroup$ – Jeromy Anglim Sep 27 '11 at 11:39
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Overview of simple slopes analysis

  • The points used to generate a graph for a simple slopes analyses are predicted values of the dependent variable given the model and various values of the predictor variables (see here for an example).

Are negative predicted values possible?

  • Yes. A regression equation can give rise to negative predicted values.
  • For example, if the equation was $Y = 1 - 2X -3Z - 1XZ$, then predicted $Y$ at $X=1$ and $Z=1$ is $Y = 1 - 2(1) -3(1) - 1(1)(1)$ or $1 -2 -3 - 1=-5$.

Do negative predicted values imply that you've done something wrong?

  • Possibly. If some or all of the following apply then negative predicted values might be a red flag on your analysis:

    1. the range of the dependent variable is all positive, and particularly if the values are a long way from 0.
    2. the correlation between predictors is not huge
    3. you have chosen appropriate values of predictors.
  • When performing a simple slopes analysis typical values for predictor values include:

    • continuous predictors that are part of the moderator effect: values drawn from plus or minus one or often two standard deviations above and below the mean or something similar.

    • categorical predictors that are part of the moderator effect: each of the values that the categorical predictor takes

    • continuous covariates: the mean of the covariate
    • categorical covariates: one of the categories

Thus, choosing predictor values consistent with the above prescriptions will generally give rise to predictions on the dependent variable that are in the ballpark of the range of the dependent variable. Of course, there are situations that could legitimately give rise to negative values even when the range of the dependent variable includes all positive values. This might be related to non-normal errors, correlated predictors, etc.

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