miive: Model-implied instrumental variable (MIIV) estimation

Description Usage Arguments Details References See Also Examples

View source: R/miive.R

Description

Estimate structural equation models using model-implied instrumental variables (MIIVs).

Usage

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miive(model = model, data = NULL, instruments = NULL, sample.cov = NULL,
  sample.mean = NULL, sample.nobs = NULL, sample.cov.rescale = TRUE,
  estimator = "2SLS", se = "standard", bootstrap = 1000L,
  boot.ci = "norm", missing = "listwise", est.only = FALSE,
  var.cov = FALSE, miiv.check = TRUE, ordered = NULL,
  sarg.adjust = "none", overid.degree = NULL,
  overid.method = "minimum.eigen")

Arguments

model

A model specified using lavaan model syntax or a miivs object returned by the miivs function. See Details for more information about permissible operators and example model syntax.

data

A data frame, list or environment or an object coercible by as.data.frame to data frame. The most common application is to supply a data.frame.

instruments

This allows user to specify the instruments for each equation. See Details and the miivs.out argument of summary.miivs for more information on the correct input format. External (auxiliary) instruments can be supplied, however, the miiv.check argument must be set to FALSE. In the typical application, the program will choose the MIIVs for each equation based on the model specification. To view the model implied instruments after estimation see the eq.info argument of summary.miive.

sample.cov

Numeric matrix. A sample variance-covariance matrix. The rownames and colnames attributes must contain all the observed variable names indicated in the model syntax.

sample.mean

A sample mean vector. If sample.cov is provided and the sample.mean argument is NULL, intercepts for all endogenous variables will not be estimated.

sample.nobs

Number of observations in the full data frame.

sample.cov.rescale

If TRUE, the sample covariance matrix provided by the user is internally rescaled by multiplying it with a factor (N-1)/N.

estimator

Options "2SLS" or "GMM" for estimating the model parameters. Default is "2SLS". Currently, only 2SLS is supported.

se

If "standard", asymptotic standard errors are computed. If "bootstrap" (or "boot"), bootstrap standard errors are computed.

bootstrap

Number of bootstrap draws, if bootstrapping is used. The default is 1000

boot.ci

Method for calculating bootstrap confidence intervals. Options are normal approximation ("norm"), basic bootstrap interval ("basic"), percentile interval ("perc"), and adjusted bootstrap percentile ("bca"). The default is normal approximation. See boot.ci for more information.

missing

Default is "listwise" however, a maximum likelihood related missing data method called "twostage" is also available. See Details below on missing for more information.

est.only

If TRUE, only the coefficients are returned.

var.cov

If TRUE, variance and covariance parameters are estimated.

miiv.check

Default is TRUE. miiv.check provides a check to determine whether user-upplied instruments are implied by the model specification (e.g. valid MIIVs). When auxiliary or external instruments are provided miiv.check should be set to FALSE.

ordered

A vector of variable names to be treated as ordered factors in generating the polychoric correlation matrix and subsequent PIV estimates. See details on ordered below for more information.

sarg.adjust

Adjusment methods used to adjust the p-values associated with the Sargan test due to multiple comparisons. Defaults is none. For options see p.adjust.

overid.degree

A numeric value indicating the degree of overidentification to be used in estimation.

overid.method

The method by which excess MIIVs should be pruned to satisfy the overid.degree. Options include the minimum eigenvalue statistic of Cragg and Donald (1993) (minimum.eigen) or Shea's Partial R-Square (1997) (partial.R2).The default is minimum.eigen.

Details

Sargan's Test of Overidentification

An essential ingredient in the MIIV-2SLS approach is the application of overidentification tests when a given model specification leads to an excess of instruments. Empirically, overidentification tests are used to evalulate the assumption of orthogonality between the instruments and equation residuals. Rejection of the null hypothesis implies a deficit in the logic leading to the instrument selection. In the context of MIIV-2SLS this is the model specification itself. By default, MIIVsem provides Sargan's overidentification test (Sargan, 1958) for each overidentified equation in the system. When cross-equation restrictions or missing data are present the properties of the test are not known. When the system contains many equations the sarg.adjust option provides methods to adjust the p-values associated with the Sargan test due to multiple comparisons. Defaults is none. For other options see p.adjust.

References

Bollen, K. A. (1996). An Alternative 2SLS Estimator for Latent Variable Models. Psychometrika, 61, 109-121.

Bollen, K. A. (2001). Two-stage Least Squares and Latent Variable Models: Simultaneous Estimation and Robustness to Misspecifications. In R. Cudeck, S. Du Toit, and D. Sorbom (Eds.), Structural Equation Modeling: Present and Future, A Festschrift in Honor of Karl Joreskog (pp. 119-138). Lincoln, IL: Scientific Software.

Bollen, K. A., & Maydeu-Olivares, A. (2007). A Polychoric Instrumental Variable (PIV) Estimator for Structural Equation Models with Categorical Variables. Psychometrika, 72(3), 309.

Freedman, D. (1984). On Bootstrapping Two-Stage Least-Squares Estimates in Stationary Linear Models. The Annals of Statistics, 12(3), 827<e2><80><93>842.

Greene, W. H. (2000). Econometric analysis. Upper Saddle River, N.J: Prentice Hall.

Hayashi, F. (2000). Econometrics. Princeton, NJ: Princeton University Press

Sargan, J. D. (1958). The Estimation of Economic Relationships using Instrumental Variables. Econometrica, 26(3), 393<e2><80><93>415.

Savalei, V. (2010). Expected versus Observed Information in SEM with Incomplete Normal and Nonnormal Data. Psychological Methods, 15(4), 352<e2><80><93>367.

Savalei, V., & Falk, C. F. (2014). Robust Two-Stage Approach Outperforms Robust Full Information Maximum Likelihood With Incomplete Nonnormal Data. Structural Equation Modeling: A Multidisciplinary Journal, 21(2), 280<e2><80><93>302.

See Also

MIIVsemmiivs

Examples

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# Example 1

bollen1989a_model <- '

    Eta1 =~ y1 + y2  + y3  + y4  
    Eta2 =~ y5 + y6  + y7  + y8    
    Xi1  =~ x1 + x2 + x3 

    Eta1 ~ Xi1  
    Eta2 ~ Xi1 
    Eta2 ~ Eta1 

    y1   ~~ y5
    y2   ~~ y4
    y2   ~~ y6
    y3   ~~ y7
    y4   ~~ y8
    y6   ~~ y8 

  '


# Example 2

bollen1989a_model <- '

    Eta1 =~ y1 + y2  + y3  + y4  
    Eta2 =~ y5 + y6  + y7  + y8    
    Xi1  =~ x1 + x2 + x3 

    Eta1 ~ Xi1  
    Eta2 ~ Xi1 
    Eta2 ~ Eta1 

    y1   ~~ y5
    y2   ~~ y4
    y2   ~~ y6
    y3   ~~ y7
    y4   ~~ y8
    y6   ~~ y8 
'

my_instruments <- ' 
    y1 ~ x2 + x3                            
    y5 ~ y2 + y3 + y4 + x2              
    y2 ~ y3 + y7 + y8 + x2           
    y3 ~ y2 + y4 + y6 + y8        
    y4 ~ y3 + y6           
    y6 ~ y3 + y4 + y7 + x2            
    y7 ~ y2 + y4 + y6 + y8       
    y8 ~ y2 + y3 + y7 + x2          
    x2 ~ y1 + y5 + y2 + y3 + y4 + y6
    x3 ~ y1 + y5 + y2 + y3 + y4 + y6
'

miive(model = bollen1989a_model, 
      data = bollen1989a, 
      instruments = my_instruments)
# Example 3

bollen1989a_model_r <- '

    Eta1 =~ y1 + l2*y2  + l3*y3  + l4*y4  
    Eta2 =~ y5 + l2*y6  + l3*y7  + l4*y8    
    Xi1  =~ x1 + x2 + 0.5*x3 

    Eta1 ~ Xi1  
    Eta2 ~ Xi1 
    Eta2 ~ Eta1 

    y1   ~~ y5
    y2   ~~ y4
    y2   ~~ y6
    y3   ~~ y7
    y4   ~~ y8
    y6   ~~ y8

'

miive(model = bollen1989a_model_r, data = bollen1989a)

zackfisher/MIIVsem documentation built on June 26, 2017, 8:22 p.m.