# eqMI.ncp: Obtain noncentrality parameter of a chisquare distribution In gabriellajg/equaltestMI: Measurement Invariance via Equivalence Testing and Projection Method

## Description

Calculate the noncentrality parameter as well as the model missipecification epsilon_t given its lower-tail critical value.

## Usage

 `1` ```eqMI.ncp(T, df, N, m, alpha = 0.05) ```

## Arguments

 `T` A chi-square statistic `df` Degrees of freedom `N` Total sample size of all groups `m` Number of groups `alpha` Significance level. Default at 0.05.

## Details

This function is to compute the noncentrality parameter `ncp`, the model missipecification `epsilon_t`, and its corresponding `RMSEA_t`. With equivalence testing, the model missipecification is also the minimum tolerable size that a researcher needs to tolerate if one wishes to proceed with further restricted tests. The formula from Venables (1975) is used for obtaining the noncentrality parameter of a non-central chi-square distribution given its lower-tail critical value.

## Value

The noncentrality parameter `ncp`, the minimum tolerable size `epsilon_t`, and `RMSEA_t` under equivalence testing.

## References

Yuan, K. H., & Chan, W. (2016). Measurement invariance via multigroup SEM: Issues and solutions with chi-square-difference tests. Psychological methods, 21(3), 405-426.

## Examples

 ```1 2 3 4 5 6 7 8 9``` ```alpha <- .05 n_1 <- 200 n_2 <- 200 N <- n_1 + n_2 m <- 2 # A made-up likelihood-ratio statistic T_ml <- 8.824 df <- 6 eqMI.ncp(T = T_ml, df = df, N = N, m = m, alpha = alpha) ```

gabriellajg/equaltestMI documentation built on Oct. 2, 2018, 8:11 a.m.