Estudio de las propiedades psicométricas del Brief COPE
http://www.scielo.org.co/scielo.php?script=sci_arttext&pid=S...
by M Reich · 2016 · Cited by 2 — The use of the Brief COPE for research purposes in Uruguayan female ... Los recursos de afrontamiento son características personales y de manejo social en los que se ... Con este objetivo, usamos la raíz cuadrática residual (RMCR) y el índice ... British Journal of Mathematical and Statistical Psychology, 45, 19-30. doi: ...
Con este objetivo, usamos la raíz cuadrática residual (RMCR) y el índice gamma o GFI (Lloret-Segura et al., 2014, p. 1 162). Se utilizó la raíz media cuadrática residual (RMCR), que indica la magnitud media de las correlaciones residuales. Valores menores o iguales a 0,05 son indicativos de que el ajuste del modelo es aceptable; según el criterio de Kelley (1935), el error típico de un coeficiente de correlación de cero en la población es aproximadamente 1/√N, donde N es el tamaño de la muestra. Si la RMCR se mueve en torno a este valor, se puede interpretar que el ajuste del modelo es aceptable. En segundo lugar, se tomó el índice GFI de Tanaka y Huba (1985).

https://en.wikipedia.org/wiki/Root-mean-square_deviation
The root-mean-square deviation (RMSD) or root-mean-square error (RMSE) is a frequently used measure of the differences between values (sample or population values) predicted by a model or an estimator and the values observed. The RMSD represents the square root of the second sample moment of the differences between predicted values and observed values or the quadratic mean of these differences. ***These deviations are called residuals*** when the calculations are performed over the data sample that was used for estimation and are called errors (or prediction errors) when computed out-of-sample. The RMSD serves to aggregate the magnitudes of the errors in predictions for various data points into a single measure of predictive power. RMSD is a measure of accuracy, to compare forecasting errors of different models for a particular dataset and not between datasets, as it is scale-dependent.[1]


the root mean square - Translation into Spanish - examples ...https://context.reverso.net › translation › english-spanish
En otras palabras, podemos decir que la raíz media cuadrática es una ... index (​GFI), the comparative fit index (CFI), and the root mean square residual (RMSR).



root mean square residual (RMSR) - Allie: Related PubMed Info .http://allie.dbcls.jp › pubmed › RMSR
http://allie.dbcls.jp/pubmed/RMSR;root-mean-squared-residual...
Search for abbreviations and long forms in lifescience, results along with the related PubMed / MEDLINE information and co-occurring abbreviations.
Abbreviation : RMSR
Long Form : root-mean-squared-residual

raíz media cuadrática residual (RMCR) > root-mean-square(d)-residual (root mean square residual) (RMSR)



***Note your text appears to omit "media" (raíz cuadrática residual - RCR). A possible omission? ***

This reference equates 'raíz cuadrática residual' to RMR which it explains as 'Raíz media residual'. The mention of this in the (translated) English abstract calls it the 'residual quadratic root', which looks like a direct translation rather than a correct translation.
https://repositorio.ucv.edu.pe/bitstream/handle/20.500.12692...

However, many articles such as this one say that RMR is 'Root Mean Square Residual'
http://www.stats.ox.ac.uk/~snijders/mpr_Schermelleh.pdf

This next reference says that 'raíz cuadrática residual' = RMCR, but in the next sentence, it says that 'raíz media cuadrática residual' = RMCR,
"Con este objetivo, usamos la raíz cuadrática residual (RMCR) y el índice gamma o GFI (Lloret-Segura et al., 2014, p. 1 162). Se utilizó la raíz media cuadrática residual (RMCR), que indica la magnitud media de las correlaciones residuales."
https://revistas.urosario.edu.co/xml/799/79947707014/html/in...

This next one says that 'raíz cuadrática residual' is RMCR -
"Finalmente, con el objetivo de analizar que las correlaciones residuales sean igual a 0, es decir, que el número de factores comunes sea el adecuado se verificaron los índices RMCR (raíz cuadrática residual) y GFI (índice gamma)."
https://repositorioacademico.upc.edu.pe/bitstream/handle/107...

This paper is a study of a Spanish version of a questionnaire but is published in English, and it equates RMCR to 'root mean square root of the residuals' (!?!?!!).
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7967561/

This reference says that 'raíz media cuadrática residual' (which in a previous reference above was described as RMCR) is the same as Root Mean Square of Residuals.
https://docplayer.es/amp/40338343-Resolucion-del-ejercicio.h...

Yet another publication calls 'Raíz Cuadrática Residual Estandarizada', SRMR, which it says is 'Standardized Root Mean Square Residual' in English
https://www.researchgate.net/publication/341447906_Validacio...

However, this one says that SRMR stands for 'Raíz media cuadrática residual estandarizada'
https://www.uv.es/lisis/terebel/2017/2017ijchp-spanish.pdf

This last reference states that 'root mean residual' is RMR and 'standardized root mean residual' is SRMR.
https://psu-psychology.github.io/psy-597-sem-sp2019/08_fit/s...

So, there is so much variation in both the English and Spanish texts, I wouldn't like to speculate on whether 'root mean residual' or 'root mean square residual' is the correct term, but I would suspect it's one of these two!