semTools (version 0.5-6)

AVE: Calculate average variance extracted

Description

Calculate average variance extracted (AVE) per factor from `lavaan` object

Usage

AVE(object, obs.var = TRUE, omit.imps = c("no.conv", "no.se"),
  omit.factors = character(0), dropSingle = TRUE, return.df = TRUE)

Arguments

object

A '>lavaan or '>lavaan.mi object, expected to contain only exogenous common factors (i.e., a CFA model). Cross-loadings are not allowed and will result in NA for any factor with indicator(s) that cross-load.

obs.var

logical indicating whether to compute AVE using observed variances in the denominator. Setting FALSE triggers using model-implied variances in the denominator.

omit.imps

character vector specifying criteria for omitting imputations from pooled results. Can include any of c("no.conv", "no.se", "no.npd"), the first 2 of which are the default setting, which excludes any imputations that did not converge or for which standard errors could not be computed. The last option ("no.npd") would exclude any imputations which yielded a nonpositive definite covariance matrix for observed or latent variables, which would include any "improper solutions" such as Heywood cases. NPD solutions are not excluded by default because they are likely to occur due to sampling error, especially in small samples. However, gross model misspecification could also cause NPD solutions, users can compare pooled results with and without this setting as a sensitivity analysis to see whether some imputations warrant further investigation.

omit.factors

character vector naming any common factors modeled in object whose indicators' AVE is not of interest.

dropSingle

logical indicating whether to exclude factors defined by a single indicator from the returned results. If TRUE (default), single indicators will still be included in the total column when return.total = TRUE.

return.df

logical indicating whether to return reliability coefficients in a data.frame (one row per group/level), which is possible when every model block includes the same factors (after excluding those in omit.factors and applying dropSingle).

Value

numeric vector of average variance extracted from indicators per factor. For models with multiple "blocks" (any combination of groups and levels), vectors may be returned as columns in a data.frame with additional columns indicating the group/level (see return.df= argument description for caveat).

Details

The average variance extracted (AVE) can be calculated by

$$ AVE = \frac{\bold{1}^\prime \textrm{diag}\left(\Lambda\Psi\Lambda^\prime\right)\bold{1}}{\bold{1}^\prime \textrm{diag}\left(\hat{\Sigma}\right) \bold{1}}, $$

Note that this formula is modified from Fornell & Larcker (1981) in the case that factor variances are not 1. The proposed formula from Fornell & Larcker (1981) assumes that the factor variances are 1. Note that AVE will not be provided for factors consisting of items with dual loadings. AVE is the property of items but not the property of factors. AVE is calculated with polychoric correlations when ordinal indicators are used.

References

Fornell, C., & Larcker, D. F. (1981). Evaluating structural equation models with unobservable variables and measurement errors. Journal of Marketing Research, 18(1), 39--50. 10.2307/3151312

See Also

compRelSEM for composite reliability estimates

Examples

# NOT RUN {
data(HolzingerSwineford1939)
HS9 <- HolzingerSwineford1939[ , c("x7","x8","x9")]
HSbinary <- as.data.frame( lapply(HS9, cut, 2, labels=FALSE) )
names(HSbinary) <- c("y7","y8","y9")
HS <- cbind(HolzingerSwineford1939, HSbinary)

HS.model <- ' visual  =~ x1 + x2 + x3
              textual =~ x4 + x5 + x6
              speed   =~ y7 + y8 + y9 '

fit <- cfa(HS.model, data = HS, ordered = c("y7","y8","y9"), std.lv = TRUE)

## works for factors with exclusively continuous OR categorical indicators
AVE(fit) # uses observed (or unconstrained polychoric/polyserial) by default
AVE(fit, obs.var = FALSE)


## works for multigroup models and for multilevel models (and both)
data(Demo.twolevel)
## assign clusters to arbitrary groups
Demo.twolevel$g <- ifelse(Demo.twolevel$cluster %% 2L, "type1", "type2")
model2 <- ' group: type1
  level: within
    fac =~ y1 + L2*y2 + L3*y3
  level: between
    fac =~ y1 + L2*y2 + L3*y3

group: type2
  level: within
    fac =~ y1 + L2*y2 + L3*y3
  level: between
    fac =~ y1 + L2*y2 + L3*y3
'
fit2 <- sem(model2, data = Demo.twolevel, cluster = "cluster", group = "g")
AVE(fit2)

# }