Print an 'indirect' Class Object

Print the content of the output of indirect_effect() or cond_indirect().

Usage

# S3 method for class 'indirect'
print(
  x,
  digits = 3,
  pvalue = NULL,
  pvalue_digits = 3,
  se = NULL,
  level = 0.95,
  se_ci = TRUE,
  wrap_computation = TRUE,
  ...
)

Arguments

x: The output of indirect_effect() or cond_indirect().
digits: Number of digits to display. Default is 3.
pvalue: Logical. If TRUE, asymmetric p-values based on bootstrapping will be printed if available. Default to FALSE if confidence intervals have already computed. Default to TRUE if no confidence intervals have been computed and the original standard errors are to be used. See Details on when the original standard errors will be used by default. Default is NULL and its value determined as stated above.
pvalue_digits: Number of decimal places to display for the p-value. Default is 3.
se: Logical. If TRUE and confidence interval has been formed, the standard error of the estimates are also printed. It is simply the standard deviation of the bootstrap estimates or Monte Carlo simulated values, depending on the method used to form the confidence intervals. Default to FALSE if confidence interval has been formed. Default to TRUE if no confidence interval has been computed and the original standard errors are to be used. See Details on when the original standard errors will be used by default. Default is NULL and its value determined as stated above.
level: The level of confidence for the confidence interval computed from the original standard errors. Used only for paths without mediators and both x- and y-variables are not standardized.
se_ci: Logical. If TRUE and confidence interval has not been computed, the function will try to compute them from stored standard error if the original standard error is to be used. Ignored if confidence interval has already been computed. Default to TRUE.
wrap_computation: Logical. If TRUE, the default, long computational symbols and values will be wrapped to fit to the screen width.
...: Other arguments. Not used.

Value

x is returned invisibly. Called for its side effect.

Details

The print method of the indirect-class object.

If bootstrapping confidence interval was requested, this method has the option to print a p-value computed by the method presented in Asparouhov and Muthén (2021). Note that this p-value is asymmetric bootstrap p-value based on the distribution of the bootstrap estimates. It is not computed based on the distribution under the null hypothesis.

For a p-value of a, it means that a 100(1 - a)% bootstrapping confidence interval will have one of its limits equal to 0. A confidence interval with a higher confidence level will include zero, while a confidence interval with a lower confidence level will exclude zero.

We recommend using confidence interval directly. Therefore, p-value is not printed by default. Nevertheless, users who need it can request it by setting pvalue to TRUE.

Using Original Standard Errors

If these conditions are met, the stored standard error, if available, will be used to test an effect and form it confidence interval:

Confidence interval has not been formed (e.g., by bootstrapping or Monte Carlo).
The path has no mediators.
The model has only one group.
Both the x-variable and the y-variable are not standardized.

If the model is fitted by OLS regression (e.g., using stats::lm()), then the variance-covariance matrix of the coefficient estimates will be used, and the p-value and confidence interval are computed from the t statistic.

If the model is fitted by structural equation modeling using lavaan, then the variance-covariance computed by lavaan will be used, and the p-value and confidence interval are computed from the z statistic.

Caution

If the model is fitted by structural equation modeling and has moderators, the standard errors, p-values, and confidence interval computed from the variance-covariance matrices for conditional effects can only be trusted if all covariances involving the product terms are free. If any some of them are fixed, for example, fixed to zero, it is possible that the model is not invariant to linear transformation of the variables.

References

Asparouhov, A., & Muthén, B. (2021). Bootstrap p-value computation. Retrieved from https://www.statmodel.com/download/FAQ-Bootstrap%20-%20Pvalue.pdf

Examples


library(lavaan)
dat <- modmed_x1m3w4y1
mod <-
"
m1 ~ a1 * x   + b1 * w1 + d1 * x:w1
m2 ~ a2 * m1  + b2 * w2 + d2 * m1:w2
m3 ~ a3 * m2  + b3 * w3 + d3 * m2:w3
y  ~ a4 * m3  + b4 * w4 + d4 * m3:w4
"
fit <- sem(mod, dat,
           meanstructure = TRUE, fixed.x = FALSE,
           se = "none", baseline = FALSE)
est <- parameterEstimates(fit)

wvalues <- c(w1 = 5, w2 = 4, w3 = 2, w4 = 3)

indirect_1 <- cond_indirect(x = "x", y = "y",
                            m = c("m1", "m2", "m3"),
                            fit = fit,
                            wvalues = wvalues)
indirect_1
#> 
#> == Conditional Indirect Effect   ==
#>                                                                             
#>  Path:                        x -> m1 -> m2 -> m3 -> y                      
#>  Moderators:                  w1, w2, w3, w4                                
#>  Conditional Indirect Effect: 1.176                                         
#>  When:                        w1 = 5.000, w2 = 4.000, w3 = 2.000, w4 = 3.000
#> 
#> Computation Formula:
#>   (b.m1~x + (b.x:w1)*(w1))*(b.m2~m1 + (b.m1:w2)*(w2))*(b.m3~m2 +
#>   (b.m2:w3)*(w3))*(b.y~m3 + (b.m3:w4)*(w4))
#> 
#> Computation:
#>   ((0.46277) + (0.23380)*(5.00000))*((0.36130) +
#>   (0.13284)*(4.00000))*((0.68691) + (0.10880)*(2.00000))*((0.40487) +
#>   (0.16260)*(3.00000))
#> 
#> Coefficients of Component Paths:
#>   Path Conditional Effect Original Coefficient
#>   m1~x              1.632                0.463
#>  m2~m1              0.893                0.361
#>  m3~m2              0.905                0.687
#>   y~m3              0.893                0.405
#> 

dat <- modmed_x1m3w4y1
mod2 <-
"
m1 ~ a1 * x
m2 ~ a2 * m1
m3 ~ a3 * m2
y  ~ a4 * m3 + x
"
fit2 <- sem(mod2, dat,
            meanstructure = TRUE, fixed.x = FALSE,
            se = "none", baseline = FALSE)
est <- parameterEstimates(fit)

indirect_2 <- indirect_effect(x = "x", y = "y",
                              m = c("m1", "m2", "m3"),
                              fit = fit2)
indirect_2
#> 
#> == Indirect Effect  ==
#>                                           
#>  Path:            x -> m1 -> m2 -> m3 -> y
#>  Indirect Effect: 0.071                   
#> 
#> Computation Formula:
#>   (b.m1~x)*(b.m2~m1)*(b.m3~m2)*(b.y~m3)
#> 
#> Computation:
#>   (0.52252)*(0.39883)*(0.80339)*(0.42610)
#> 
#> Coefficients of Component Paths:
#>   Path Coefficient
#>   m1~x       0.523
#>  m2~m1       0.399
#>  m3~m2       0.803
#>   y~m3       0.426
#> 
print(indirect_2, digits = 5)
#> 
#> == Indirect Effect  ==
#>                                           
#>  Path:            x -> m1 -> m2 -> m3 -> y
#>  Indirect Effect: 0.07134                 
#> 
#> Computation Formula:
#>   (b.m1~x)*(b.m2~m1)*(b.m3~m2)*(b.y~m3)
#> 
#> Computation:
#>   (0.52252)*(0.39883)*(0.80339)*(0.42610)
#> 
#> Coefficients of Component Paths:
#>   Path Coefficient
#>   m1~x     0.52252
#>  m2~m1     0.39883
#>  m3~m2     0.80339
#>   y~m3     0.42610
#>