Dear @Bram Having 10-20 observations for each variable refers to observed items not latent factor or composite variable. For example, in a study, we have four variables each measured by five observed items thus making it 5×4 = 20 observed items. Now, as per so called rule of thumb for applying regression/path analysis/SEM, required sample would be 20 items multiplied by 10 observations (going with the lowest) which results into 200 observations/responses.

Imran Anwar Thanks for your answer! I am also curious to the reasoning behind the rule of thumb rule. Does it have something to do with gaining sufficient degrees of freedom? And so yes, why is it so important to have sufficient degrees of freedom?

La muestra (N) tiene que ser representativa en número y en las variables de persona: edad y sexo o género; pero también en todas aquellas variables que sean transcendentes para conseguir el objetivo general y específicos así como para comprobar las hipótesis nula y alternativa. Lógicamente, cuando mayor sea la muestra mayores posibilidades de encontrar significación estadística y, por tanto, mejor para controlar el azar...

Bram -

This is for regression, not a single univariate data set. You can't apply a 'formula' designed for something else. But the principle is the same in that you want to know what sample size will achieve the accuracy level you want. In a single data set, you could estimate the population standard deviation, and then see, under the methodology employed, what sample size will give you a desired standard error value, or lower, for a mean or whatever is of interest. But regression is more complex.

In regression you are looking at conditional distributions of y-values, such that if you plot predicted-y on the x-axis, and estimated residuals on the y-axis, the variance of those estimated residuals in the vertical direction is a big part of the variance of yi given predicted-yi. The estimated variance of the prediction error depends on the model coefficient standard errors and especially on the sigma of the estimated residuals. It differs in each case, especially when there is heteroscedasticity of the estimated residuals. Also, here, as in other sample size requirements determinations, we are assuming no bias. But if the model were missing a key predictor ('independent') variable, that would generally produce bias. (If an unneeded predictor were added, that generally increases variance.)

With a regression that has large p, not p-value, but the number of predictors plus one if there is an intercept term, then the degrees of freedom is n-p. I suspect that perhaps a large number of predictors (only use what is necessary, no more, no less, no substitutions which are not necessary) may mean that the estimated variance of the prediction error in each case may need a larger sample to even stabilize the variance estimates. But the key is not the degrees of freedom, but the variance estimates.

First you need to see if your model, or another, does well in a "graphical residual analysis." Then a "cross-validation" may help you not to model to fit too closely to a particular sample rather than to the population or subpopulation in general for which you wish your model to apply. If you are reasonably certain that your model is adequate, then you may see how well it performs regarding the cases of interest to you.

You might be interested in the following, where a simple model, using the classical ratio estimator, is considered, and we want to predict a total, so all data not in the sample for this one item, one subpopulation or population, are all predicted:

https://www.researchgate.net/publication/261947825_Projected_Variance_for_the_Model-based_Classical_Ratio_Estimator_Estimating_Sample_Size_Requirements.

.....

In general, the sample size required to have the accuracy you want depends on defining exactly what you want, and I think in some cases may need to be found iteratively - adding data as needed.

Cheers. - Jim

Evidentemente después de análisis univariante, viene el bivariante y, finalmente, el multivariante para establecer las variables transcendentes ante el evento estudiado...

I find these rules of thumb anachronistic and often too simple (one dimensional) for the modelling we are actually trying to do. For example in regression the number of observations needed depends how collinear the variables are, and you need to take this into account. A much better way is to simulate data with known properties and see if you favoured technique (given the number of observations and number and nature of the variables ) can in practice extract the correct signal from the noise.- this is often very sobering. For discussion and software that can do this see http://www.bristol.ac.uk/media-library/sites/cmm/migrated/documents/mlpowsim-manual.pdf