Structural Equation Modeling: Applications Using Mplus

7.1 The Rules of Thumb for Sample Size Needed for SEM

Although determination of appropriate sample size is a critical issue in SEM, unfortunately, there is no consensus in the literatureregarding what would be the appropriate sample size for SEM. Some evidence exists that simple SEM models could be meaningfully tested even if sample size is quite small (Hoyle, 1999; Hoyle and Kenny, 1999; Marsh and Hau, 1999), but usually, N = 100–150 is considered the minimum sample size for conducting SEM (Tinsley and Tinsley, 1987; Anderson and Gerbing, 1988; Ding, Velicer, and Harlow, 1995; Tabachnick and Fidell, 2001). Some researchers consider an even larger sample size for SEM, for example, N = 200 (Hoogland and Boomsma 1998; Boomsma and Hoogland, 2001; Kline, 2005). Simulation studies show that with normally distributed indicator variables and no missing data, a reasonable sample size for a simple CFA model is about N = 150 (Muthén and Muthén, 2002). For multi-group modeling, the rule of thumb is 100 cases/observations per group (Kline, 2005).

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 (Nunnally, 1967).

Very often attention is given to the ratio of (N:q) of ...