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Sample Size Planning for Structural Equation Modeling From the Power Analysis Perspective

Source: R/ss_power_sem.R
ss_power_sem.Rd

Calculate the necessary sample size for an SEM study, so as to have enough power to reject the null hypothesis that (a) the model has perfect fit, or (b) the difference in fit between two nested models equal some specified amount.

Usage

ss_power_sem(
  F_ML = NULL,
  df = NULL,
  RMSEA_null = NULL,
  RMSEA_true = NULL,
  F_full = NULL,
  F_res = NULL,
  RMSEA_full = NULL,
  RMSEA_res = NULL,
  df_full = NULL,
  df_res = NULL,
  alpha_level = 0.05,
  desired_power = 0.85
)

Arguments

F_ML

The true maximum likelihood fit function value in the population for the model of interest. Leave this argument NULL if you are doing nested model significance tests

df

The degrees of freedom of the model of interest. Leave this argument NULL if you are doing nested model significance tests

RMSEA_null

The model's population RMSEA under the null hypothesis. Leave this argument NULL if you are doing nested model significance tests

RMSEA_true

The model's population RMSEA under the alternative hypothesis. This should be the model's true population RMSEA value. Leave this argument NULL if you are doing nested model significance tests

F_full

The maximum likelihood fit function value for the full model

F_res

The maximum likelihood fit function value for the restricted model

RMSEA_full

The population RMSEA value for the full model

RMSEA_res

The population RMSEA value for the restricted model

df_full

The degrees of freedom for the full model

df_res

The degrees of freedom for the restricted model

alpha_level

The Type I error rate. Defaults to 0.05.

desired_power

The desired power. Defaults to 0.85, matching the rest of the ss_power_* family.

Value

A data.frame with a necessary_N row, the smallest integer N whose power reaches desired_power under the supplied fit-function or RMSEA alternative, and an actual_power row giving the realized power at that N.

References

MacCallum, R. C., Browne, M. W., & Sugawara, H. M. (1996). Power analysis and determination of sample size for covariance structure modeling. Psychological Methods, 1(2), 130–149. doi:10.1037/1082-989X.1.2.130

Lai, K., & Kelley, K. (2011). Accuracy in parameter estimation for targeted effects in structural equation modeling: Sample size planning for narrow confidence intervals. Psychological Methods, 16(2), 127–148. doi:10.1037/a0021764

Maxwell, S. E., Delaney, H. D., & Kelley, K. (2027). Designing experiments and analyzing data: A model comparison perspective (4th ed.). Routledge.

See also

design_consequences for what a chosen design delivers: power, the Type S (sign) and Type M (exaggeration) errors of the significance filter, and the expected confidence interval width.

Other sample size for power: power_fisher_exact(), ss_aipe_mixed_effects(), ss_power_R2(), ss_power_R2_sensitivity(), ss_power_c(), ss_power_c_ancova(), ss_power_composite_ancova(), ss_power_composite_ancova_2group(), ss_power_composite_anova(), ss_power_composite_factorial_ancova(), ss_power_composite_factorial_ancova_het(), ss_power_composite_factorial_anova(), ss_power_composite_sem(), ss_power_contrast(), ss_power_equivalence_c(), ss_power_factorial_ancova(), ss_power_factorial_anova(), ss_power_indirect_effect(), ss_power_mixed_effects(), ss_power_one_way_anova(), ss_power_pcm(), ss_power_r(), ss_power_rc(), ss_power_reg_coef(), ss_power_reg_coef_sensitivity(), ss_power_rm_anova(), ss_power_sc(), ss_power_smd(), ss_power_split_plot_anova()

Author

Ken Kelley kkelley@nd.edu

Examples

# One-model test: necessary N to reject H0: RMSEA = 0 in favor of
# a model whose population RMSEA is 0.05 at 80% power, alpha = .05,
# with df = 20.
ss_power_sem(RMSEA_null = 0, RMSEA_true = 0.05, df = 20,
             alpha_level = 0.05, desired_power = 0.80)
#>  term         value
#>  necessary_N  421  
#>  actual_power 0.801

# Equivalent input via the population fit function: F_ML = df * RMSEA^2.
ss_power_sem(F_ML = 20 * 0.05^2, df = 20, alpha_level = 0.05, desired_power = 0.80)
#>  term         value
#>  necessary_N  421  
#>  actual_power 0.801

# Two-model nested test: necessary N to detect the difference
# between a full model (RMSEA = 0.04, df = 18) and a restricted
# model (RMSEA = 0.06, df = 22) at 80% power.
ss_power_sem(RMSEA_full = 0.04, df_full = 18,
             RMSEA_res = 0.06, df_res = 22,
             alpha_level = 0.05, desired_power = 0.80)
#>  term         value
#>  necessary_N  238  
#>  actual_power 0.8