Statistically there is no difference. However, sometimes it makes the interpretation easier due to it's link with the theory you use and your hypotheses.

Dear Heather,

The consequences can be assessed as follows. I assume a linear model, in which the dependent variable y is a function of an independent variable x via y = a + bx. Both y and x reflect variables measured in individual persons. For the sake of the argument, let us assume that x denotes the sex of a person, coded as 1 for women, and 0 for men. We estimate b as 3.14, say. The interpretation is that y increases by 3.14 units when we increase x by one unit. In other words, women score 3.4 points higher on y than men do (other things remaining the same, in particular when there are additional regressors).

Now we replace, for whatever reason, x by a variable z, coded as 1 for men and 0 for women. In other words, z = 1 - x, or x = 1 - z. Since the true relationship still is y = a + bx, we write this as y = a + b(1-z) = (a+b) - bz. When we estimate this new model, we find that the effect of z equals (-z), or -3.14. This is what you wrote. But note that the constant has changed from a to (a+b).

To code a dummy variable by values of 0 and 1 is entirely arbitrary. We can choose any (distinct) pair of values. But estimation based (0,1) coding has the easiest interpretation.

So far about the simple case of one dummy variable. The case of a categorical variable with N categories, to be represented by N-1 dummy variables, is a straightforward extension.

But perhaps your question concerns a continuous (ratio) variable, for example a firm's profit in dollars. Write the model as y = a + bx, where x is annual profit. Now assume we want to replace x by the opposite, annual losses, represented by z. In that case, z = (-x), and you estimate (-b), instead of b.

Kind regards, Nico

Hi, Heather Booth . The only reason that comes to my mind is a better interpretation. As an instance, consider this correlation; the lower use of smoke, the lower risk of cancer. The interpretation of this example may not sound great to all, as there might be many other factors increasing the risk of cancer. Now, let's imagine reverse coding. The correlation would be the higher use of smoke, the higher risk of cancer. This may sound more plausible to ears.

It could be a good idea to maintain the consistency of all scale items as regards their directionality of agreement or disagreement before undertaking any statistical analysis. To that end, negatively phrased items could be reverse scored. However, such a technique might affect score reliability if mixed stems were used in a 5-point Likert scale (Weems & Onwuegbuzie, 2001). You could go through the article by Weems and Onwuegbuzie (2001), fully cited below, for further insights.

Weems, G. H., & Onwuegbuzie, A. J. (2001). The impact of midpoint responses and reverse coding on survey data. Measurement and Evaluation in Counseling and Development, 34(3), 166–176. https://doi.org/10.1080/07481756.2002.12069033

Good luck,

Hi Heather,

Heather Booth

I wouldn't do that, if its not a mathematical necessity. It does not make much sense in my mind. The idea behind multivariate regression is usually to investigate the connection (and subsequently possibly also causality) between a target variable and a set of explanatory variables. In some cases, you might be forced to perform some mathematical transformation of the variables as the computation is not possible alternatively. For instance, if you try to estimate the log-decrease in TFR we'd expect to observe following some decrease in paid parental care time. In that example, the left-hand side of the equation would not be defined, as we cannot compute logs of negative values. Apart from mathematical problems, I would not advice on changing the sign of your variables. Normally, this makes your interpretation even more confusing, as a negative correlation between two variables is shown as such. Let's say you try to estimate Emigration flows for some country, using certain socio-demographic variables as predictors. You would, for instance, assume a negative connection between emigration flows and average income in said country, c.p, which would be reflected by a negative sign of the coefficient.

Why would you change that?

Best!

Patrizio

I think this depends to some extent on the hypothesis that is employed in the work you are conducting.

I also would not do it. As discussed above, it does not change anything regarding the fit of the model, and regarding the interpretation it is dangerous in my opinion since your readers might not be aware that you switched signs and, therefore, get the message wrong. To avoid that, you would need to specify clearly that (some of) the variables have the sign reversed, and that ends up being more cumbersome than keeping the correct sign.