I am interested to know, How to calculate the sample size in regression studies? I have read the following article: Sample Size for Multiple Regression: Obtaining Regression Coefficients That Are Accurate, Not Simply Significant.
Unfortunately, I did not understand the concepts. We ask you to guide me in the field? Thanks a lot
Sajjad,
Sample size estimates for linear regression can be vary in complexity. Much of this depends on whether your models include only fixed effects or if you are using both random and fixed effects. If your model is very basic where your are simply looking at the association of two variables with cross sectional data, the sample size estimate will be based primarily on the predictor variable's slope and standard error. Alfredo's suggestion of downloading GPower is very good. I have used GPower for 8 years and it does a good job of providing sample size estimates for studies with simple designs.
For more complex linear models, such as those with several covariates, or when a random effect is included, there are several packages for R that can be used.
I hope this information is helpful.
Mike
Dear Sajjad
Try to have a look of this site (http://www.gpower.hhu.de/). It is a free software GPower, a friend of mine (Armin Scholz) sent it to me.
Hi,
If you can understand French, you can use the book "Epidemiologie - Principes et méthodes quantitatives" by Jean Bouvier and al. from the INSERM unit 822. It is well done and easy to read and applicate.
Sajjad,
Sample size estimates for linear regression can be vary in complexity. Much of this depends on whether your models include only fixed effects or if you are using both random and fixed effects. If your model is very basic where your are simply looking at the association of two variables with cross sectional data, the sample size estimate will be based primarily on the predictor variable's slope and standard error. Alfredo's suggestion of downloading GPower is very good. I have used GPower for 8 years and it does a good job of providing sample size estimates for studies with simple designs.
For more complex linear models, such as those with several covariates, or when a random effect is included, there are several packages for R that can be used.
I hope this information is helpful.
Mike
I agree with the above users' suggestions, you need a power analysis. There are several different ways to do power analysis. For a simple design that will meet most statistical assumptions (e.g if you expect residuals to be normally distributed, etc.) than using a parametric power analyzer like GPower is generally the easiest thing. For complex designs (like the kinds Mike mentioned) or ones where you expect assumptions to be violated (e.g. if you think the data may be severely non-normal) another simple method is simulation: you create [using some programming language, like R], a fake "population" of data that has the effect size and variation you predict, and then you write a script that can draw a few thousand random samples from that population and measure the effect in those samples (i.e., doing a few thousand fake "experiments") and see what percentage of samples detected the effect at the significance level you want; that percentage is your power. You can repeat this process with several different simulated sample sizes until you find the sample size that gives you the power you want (typically people go for 80% power). For an example of what I mean, here's a simulation power analysis tool I use: https://politzerahles.shinyapps.io/ERPpowersim/ (this isn't for multiple regression, but it illustrates the same concept).
Sajjad -
In general, for sample size considerations of various types, you want to control for bias, and then find a sample size large enough to give you a suitably low standard error. Here you could seek an estimate for the variance of the prediction error, after checking for omitted variables, and doing a validation using test data. Because of heteroscedasticity, the variance of the prediction error would vary by range of a size estimator. You would want to look in the range of interest.
Your software may provide the estimates you want. For example, in SAS PROC REG, the square root of the estimated variance of the prediction error, for a given predicted y, is provided as STDI.
I have a great deal of work on my ResearchGate page extending this to work on finite populations (with simple models that could also be extended), where you need estimates ("predictions") for totals, but I assume you are looking at individual predicted y-values.
Just looking at the individual coefficients in a regression equation will not give you the information you appear to need.
Best wishes - Jim
in the name of God
dear Dr. lotfi
Hi, Good Day!
there are different methods.
a simple method for multiple regression is:
minimal requirement is a ratio of 5:1 for number of subjects to independent variables. the desired ratio is 15:1.
and for logistic regression is:
10-15 subjects per each predictor variable
best regards
tagharrobi
Sekaran (2003) wrote:
Roscoe (1975) proposes the following rules of thumb for determining sample size:
1. Sample sizes larger than 30 and less than 500 are appropriate for most research.
2. Where samples are to be broken into subsamples; (male/females, juniors/
seniors, etc.), a minimum sample size of 30 for each category is necessary.
3. In multivariate research (including multiple regression analyses), the sample size should be several times (preferably 10 times or more) as large as the number of variables in the study.
4. For simple experimental research with tight experimental controls (matched pairs, etc.), successful research is possible with samples as small as 10 to 20 in size.
References
Sekaran, U., 2003. Research methods for business: A skill building approach. John Wiley & Sons.
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