Hi Kumbirai,

it depends on model complexity but also on many other factors (e.g., normality of the data, missing patterns). Most researcher would recommend using sample sizes of at least 200/ 5 or 10 cases per parameters (see for an overview Kline, 2011, pp: 11-12).

However, two of the most recent simulations studies recommend rather small sample sizes as enough:

Wolf, E. J., Harrington, K. M., Clark, S. L., & Miller, M. W. (2013). Sample size requirements for structural equation models an evaluation of power, bias, and solution propriety. Educational and Psychological Measurement, 73(6), 913-934. doi: 10.1177/0013164413495237

They found sample size requirements ranging from 30 (Simple CFA with four indicators and loadings around .80) up to 450 cases (mediation models). 

Sideridis, G., Simos, P., Papanicolaou, A., & Fletcher, J. (2014). Using Structural Equation Modeling to Assess Functional Connectivity in the Brain Power and Sample Size Considerations. Educational and Psychological Measurement, dpi: 10.1177/0013164414525397

They found that a sample size of 50-70 would be enough for a model of functional brain connectivity involving 4 latent variables.

Maybe your model fits with one of the model setups described in the above papers. Alternatively, it is always best to run your own Monte Carlo- study:

Muthén, L. K., & Muthén, B. O. (2002). How to use a Monte Carlo study to decide on sample size and determine power. Structural Equation Modeling, 9(4), 599-620. https://www.statmodel.com/download/FinalSEMsingle.pdf

Pornprasertmanit, Sunthud, et al. (2014). Package ‘simsem’.http://cran.r-project.org/web/packages/simsem/simsem.pdf

Best,

Alex

Hi, a rule of thumb says that the minimum sample size should be equal to the number of parameters to estimate in the model multiplied with 5. KR, Christian

Hi Kumbirai,

it depends on model complexity but also on many other factors (e.g., normality of the data, missing patterns). Most researcher would recommend using sample sizes of at least 200/ 5 or 10 cases per parameters (see for an overview Kline, 2011, pp: 11-12).

However, two of the most recent simulations studies recommend rather small sample sizes as enough:

Wolf, E. J., Harrington, K. M., Clark, S. L., & Miller, M. W. (2013). Sample size requirements for structural equation models an evaluation of power, bias, and solution propriety. Educational and Psychological Measurement, 73(6), 913-934. doi: 10.1177/0013164413495237

They found sample size requirements ranging from 30 (Simple CFA with four indicators and loadings around .80) up to 450 cases (mediation models). 

Sideridis, G., Simos, P., Papanicolaou, A., & Fletcher, J. (2014). Using Structural Equation Modeling to Assess Functional Connectivity in the Brain Power and Sample Size Considerations. Educational and Psychological Measurement, dpi: 10.1177/0013164414525397

They found that a sample size of 50-70 would be enough for a model of functional brain connectivity involving 4 latent variables.

Maybe your model fits with one of the model setups described in the above papers. Alternatively, it is always best to run your own Monte Carlo- study:

Muthén, L. K., & Muthén, B. O. (2002). How to use a Monte Carlo study to decide on sample size and determine power. Structural Equation Modeling, 9(4), 599-620. https://www.statmodel.com/download/FinalSEMsingle.pdf

Pornprasertmanit, Sunthud, et al. (2014). Package ‘simsem’.http://cran.r-project.org/web/packages/simsem/simsem.pdf

Best,

Alex

If you are surveying, Genreally 1:4 or 1:5 for each Item and sample ratio for CFA and Structural regression Analysis.

Hi Kumbiari,

When you want to measure a model and referring it to a society, you must to have a large sample size, but in some books noted that the min sample size is about 200, and 15 data for a variable. You can also check Tabanchik and Fidel`s (2013) point of view, Using Multivariate Statistics.

However, if you have an small sample size, you may check SmartPLS, and measuring partial least squares instead of variance-covariances.

Good luck

Thank you so much for your contributions I am finding them helpful.

A useful rule of thumb concerning the relation between sample size and model complexity that also has some empirical support was referred to by Jackson (2003) as the N:q rule. This rule is applicable when the estimation method used is maximum likelihood (ML), which is by far the method used most often in SEM. Indeed, ML is the default method in most SEM computer tools. Properties of ML estimation are described in Chapter 7, but it is no exaggeration to describe this method as the motor of SEM. (You are the driver.) In ML estimation, Jackson (2003) suggested that researchers think about minimum sample size in terms of the ratio of cases (N) to the number of model parame- ters that require statistical estimates (q). An ideal sample size-to-parameters ratio would be 20:1. For example, if a total of q = 10 model parameters require statistical estimates, then an ideal minimum sample size would be 20 × 10, or N = 200. Less ideal would be an N:q ratio of 10:1, which for the example just given for q = 10 would be a minimal sample size of 10 × 10, or N = 100. As the N:q ratio decreases below 10:1 (e.g., N = 50, q = 10 for a 5:1 ratio), so does the trustworthiness of the results.

pp 11, kline book, Principles and Practice of Structural Equation Modeling 

چندین توصیه به صورت حدس در رابطه با انتخاب تعداد نمونه وجود دارد. به طوری‏که انتخاب نمونه‎ کمتر از 100 مورد را کم و برای مدل‎های خیلی کوچک توصیه می‎کنند. اما تعداد نمونۀ 100 الی 200 را متوسط و در مدل‎هایی که خیلی پیچیده نباشند، توصیه می‎نمایند. اما در مواردی که تعداد نمونه بیش از 200 نفر انتخاب شود، این تعداد بزرگ و برای عمدۀ مدل‎ها متناسب ارزیابی شده است(کلاین، 2005).

 Real thanks to you Dr Alexandru Agache. your answer is absolutely fruitful   

You can also refer to this - Kline (2005) and Weston & Gore, (2006) it is recommended to have a minimum sample size of 200 for any SEM analysis.

Or refer to Soper's Sample size calculator. http://www.danielsoper.com/statcalc/calculator.aspx?id=89

Hi,

It depends on the amount of latent variables that you want to fit. In other words, it depends on the complexity of your models. The higher the amount of latent variables, the higher the amount of paths you make (example if you do interactions or a mediation analysis), the bigger your data should be in order to have better estimates. As mentioned before, the Kline (2011). Principles and Practice of Structural Equation Modeling, Third Edition (Methodology in the Social Sciences) is a good reference for this. 

Also, it is important to take into account that the amount of data will also influence your fit indices. You can check Hu & Bentler, (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling, Vol 6(1), 1999, 1-55. http://dx.doi.org/10.1080/10705519909540118.

Good luck!

Hi Everyone,

This is really interesting conversation. I am also struggling to determine the sample size for my study. There are 4 variables I have in my model. Safety climate (40 questions), Psychological Safety (27 questions), Safety behavior (6 questions) and Safety outcomes (4 questions). Could you please help me with any method to determine the required sample size for the study? Thank you.  

Hi all, 

You can check Hoyle [R.H. (ED.) (2012). Handbook of structural equation modeling,  Guilford Press] for a discussion on how many indicators should be included for each latent variable (p.65). Some ideas included:

̵   For a single latent variable with reflective indicators, 3

̵   When a model includes more than one latent variable and the latent variables are related, allowing for latent variables with even fewer indicators is

-  When sample size is small, estimation failures are less likely as the number of indicators per latent variables increases

I also recommend Hair et al. [Hair, Black, Babin, Anderson & Tatham. (2014). Multivariate Data Analysis, 7th Edition]. See discussion on sample size in pages 573-574. They also include some guidelines for using cutoff values for GOD indices depending on the model complexity (sample size and number of observed variables) (pp. 583-584)

Hope this helps,

Emilio

Hi Mohammad Tanvi Newaz

Try to get 'actual' outcome data, linked to the questions you are asking. They could be process variables (what people are, or are not, doing - as well as actual incident data. Self-report data is contaminated by the twin diseases of common-method variance and social-desirability responding.! If you use actual outcome data, it is much more likely for a reviewer  to recommend publication.

Thank you so much all of you. you people have solved my problem

Yes, I recommend also Hair et al. (2014).

this very interesting professional discussion.  i have tried to construct SEM for my study.  i have 5  latent variables in my model, depression (9 questions,), General anxiety (7 question), social anxiety (10 question) and PTSD (17 questions) and also somatic symptom (15 questions).  depression and anxiety are my dependent variable and used second order SEM because anxiety measured using general anxiety, social anxiety and PTSD). The sample size of this study is 217. i had conduct data cleaning activity like missing record, outlier, unengaded response and common bias and other also check sample size adequate using KMO (Kmo=0.89).  even tried to determain the SEM but the model  not fit the required mode fit criteria,  could you please help me with any think,  What is the minimum acceptable range for factor loading in SEM? Thank you.  

Dear Bekele,

As I mentioned above, check Hair et al. [Hair, Black, Babin, Anderson & Tatham. (2014). Multivariate Data Analysis, 7th Edition]. There is a discussion on sample size in pages 573-574. They also include some guidelines for using cutoff values for GOD indices depending on the model complexity (sample size and number of observed variables) (pp. 583-584).

Are your indicators normally distributed? If not, you can try a robust estimation method (e.g., using the statistical software EQS)

Sample size is often considered in light of the number of observed variables. For normally distributed data, Bentler and Chou (1987) suggest a ratio as low as 5 cases per variable would be sufficient when latent variables have multiple indicators. A widely accepted rule of thumb is 10 cases/observations per indicator variable in setting a lower bound of an adequate sample size (Nunnly 1967)

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4334479/

According to Kline (2011) a typical sample size in studies where SEM is used is about 200 cases. However, a sample size of 200 cases may be too small when analyzing a complex model.

Unfortunately the answer to this is really annoying, it is "It depends". The flexibility of SEM is that given a set of variables we can construct lots of different models, however the down-side of this is that the models can differ in complexity. So we can't work out the required sample size based on the number of variables. Also the required sample size will depend on the 'effect size', or how large the coefficients of the fitted model are. Models with large effects are 'easier' to reject, that is they would require a smaller samples size compared to a model with very small effects. A problem with SEM is there may be some very weak effects and some very strong effects in a model so some parts of the model may be adequately powered and some parts may be underpowered.

So after all this waffle I agree with Alexandru that a monte carlo based power analysis is the way forward!

Read my post about What is a good sample size for Structural Equation Modeling (SEM) here: www.sarpublisher.com/what-is-a-good-sample-size-for-structural-equation-modeling-sem/

See this page from@nedkock for a decent explanation and related references: https://warppls.blogspot.com/2014/08/minimum-sample-size-in-pls-sem.html. As an aside, I believe that there are two related issues, 1) the stability and reliability of estimates, and 2) whether the results are meaningful. If one is drawing conclusions about a sizable population from a very small sample, I have to wonder whether the results are meaningful. (That's just my view though.)

PLEASE READ THIS ARTICLE

Article Sample Size Requirements for Structural Equation Models: An ...

Alexandru Agache Can a sample size of 125 be acceptable for path analysis in AMOS, with 20 parameters?

Thanks

According to Kline (2011) a typical sample size in studies where SEM is used is about 200 cases. However, a sample size of 200 cases may be too small when analyzing a complex model

A sample of 100 epileptics are enough to run SEM

A useful rule of thumb is the N:q rule. The rule is applicable when the estimation used is Maximum Likelihood (ML). Rex B. Kline's book on Principles and practice of SEM explains it better.

If the sample is fir for SEM then it justify the population?

The more complex the model, the more samples is needed