# Why is a squared residual being called an RMSD?

I'm hoping that someone can help me understand why someone would call something an RMSD that is really just a squared residual. I'm using someone else's R script which performs simulations according to a model. The model has a free parameter that needs to be optimized, so a method is needed to determine what value for this free parameter results in a better fit. To optimize the value, two different values are compared using what the author refers to as an RMSD, which they calculate as follows:

rmsd <- (model_mean - observed_mean)^2


To determine which value for the free parameter results in a better fit, an "rmsd" is calculated for both simulations, and whichever "rmsd" is closer to zero is the better fit. This seems like a fine way to determine which of two values is better for the free parameter, I'm just puzzled because it's not an RMSD, as far as I can tell. I understand RMSD to be calculated as follows:

rmsd <- sqrt(
sum((model_mean - observed mean)^2) / n
)


This is different since it's the square root of the mean of numerous squared residuals, so I guess the only difference between this and what the author calls RMSD is that they don't get the square root. Am I missing something, or am I right in being confused about why they call a squared residual an RMSD?

Sincerely, Statistically ignorant

• Jun 20, 2021 at 19:09