Model Implied Instrumental Variable Estimation of Structural Equation Models

Description

MIIVsem is a package for estimating structural equation models using model-implied instrumental variables (MIIVs).

Author(s)

Maintainer: Zachary Fisher fish.zachary@gmail.com

Authors:

• Kenneth Bollen

• Kathleen Gates

• Mikko Rönkkö

See Also

Useful links:

• https://github.com/zackfisher/MIIVsem

• Report bugs at https://github.com/zackfisher/MIIVsem/issues

Industrialization-Democracy Data

Description

A dataset from Bollen (1989) containing measures of political democracy and industrialization for 75 developing countries in 1960 and 1965. The variables are as follows:

Usage

bollen1989a

Format

A data frame with 75 rows and 9 variables

Details

• y1. freedom of the press, 1960

• y2. freedom of political opposition, 1960

• y3. fairness of elections, 1960

• y4. effectiveness of elected legislature, 1960

• y5. freedom of the press, 1965

• y6. freedom of political opposition, 1965

• y7. fairness of elections, 1965

• y8. effectiveness of elected legislature, 1965

• x1. natural log of GNP per capita, 1960

• x2. natural log of energy consumption per capita, 1960

• x3. arcsin of square root of percentage of labor force in industry, 1960

References

Bollen, K. A. (1989). Structural equation models. New York: Wiley-Interscience.

Examples

## Not run: 
  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 devtools::build_win()
  '

## End(Not run)

Union sentiment data

Description

A dataset from McDonald and Clelland (1984) reanalyzed by Bollen (1989) containing data on union sentiment of southern nonunion textile workers.

Usage

bollen1989b

Format

A data frame with 173 rows and 5 variables

Details

• deferenc. deference (submissiveness) to managers

• laboract. support for labor activism

• unionsen. sentiment towards unions

• yrsmill. log of years spent in textile mill

• age. centered age

References

Bollen, K. A. 1989. Structural Equations with Latent Variables. New York: Wiley

McDonald, A, J., & Clelland, D. A. (1984). Textile Workers and Union Sentiment. Social Forces, 63(2), 502–521.

Examples

## Not run: 
 model <- '
   unionsen ~  deferenc + laboract + yrsmill
   deferenc ~  age
   laboract ~  age + deferenc
   yrsmill  ~~ age
 '

## End(Not run)

Subjective class data

Description

The following data is from Bollen (1989) using data from Kluegel et al. (1977). These data include measures of actual income (inc) and occupational prestige (occ), measures of respondents' subjective assessments of income (subinc), occupational prestige (subocc), and overall SES status (subgen).

Usage

bollen1989c

Format

A data frame with 432 rows and 5 variables

Details

• occ. actual occupational prestige

• inc. actual income

• subocc. respondents' subjective assessments of prestige

• subinc. respondents' subjective assessments of income

• subgen. respondents' subjective assessments of SES status

References

Bollen, K. A. 1989. Structural Equations with Latent Variables. New York: Wiley

Kluegel, J. R., Singleton, R., & Starnes, C. E. (1977). Subjective Class Identification: A Multiple Indicator Approach. American Sociological Review, 42(4), 599–611.

Examples

## Not run: 
 model <-    '
	subinc  ~ inc + subocc
   subocc  ~ occ + subinc
   subgen  ~ subinc + subocc
	subinc ~~ subocc + subgen
   subocc ~~ subgen
	inc    ~~ occ
 '

## End(Not run)

Perceived accessibility data

Description

Data come from a survey that was conducted in rural clusters of Tanzania in 1993. The goal was to collect information on the perceived accessibility of a specific family planning facility that serviced each cluster. Six informants were chosen: 3 female and 3 male. New informants were chosen for each cluster. Each informant was independently asked to rate the accessibility of the facility, and how easy it was to get to the facility. More specifically the women informants were asked to rate how women of childbearing age perceived the accessibility and easiness and men were asked to rate how accessible and easy men perceived access to the clinic to be. Higher values indicate greater accessibility and ease of travel. The female informants' ratings are 1 to 3 and the male informants' ratings are 4 to 6.

Usage

bollen1996

Format

A data frame with 220 rows and 12 variables

Details

• access1.

• access2.

• access3.

• access4.

• access5.

• access6.

• easy1.

• easy2.

• easy3.

• easy4.

• easy5.

• easy6.

References

Bollen, K. A., Speizer, I. S., & Mroz, T. A. (1996). Family Planning Facilities in Rural Tanzania: His and Her Perceptions of Time and Distance.

Examples

## Not run: 
 model <- ' 
    femaleAccess  =~ access1 + access2 + access3
    maleAccess    =~ access4 + access5 + access6
    femaleEasy    =~ easy1   + easy2   + easy3
    maleEasy      =~ easy4   + easy5   + easy6 
 '

## End(Not run)

build the missing data model syntax

Description

build the missing data model syntax

Usage

buildMissingSyntax(pt)

build the restriction matrix

Description

Function returns a list r with information regarding coefficient restrictions and estimation. The field R contains a restriction matrix for imposing cross-coefficient restrictions. If no cross-coefficient restrictions are present R is set to NULL. The vector q contains a vector of lagrangean multipliers. The vector constrained gives the constrained coefficients in convenient form.

Usage

buildRestrictMat(d)

Arguments

build the sum of squares and cross products matrix

Description

Build sum of squares and crossproducts matrix (SSCP). From the means, covariances, and n's you can recover the raw sum-of-squares and products matrix for all the variables. Say the matrix of all the variables is X, with mean vector bar(x), and covariance matrix S, based on sample-size n. Then the SSCP matrix is X'X = (n - 1)S + n bar(x) bar(x)'. You then need to add the row/column for the constant, which is just n in the 1, 1 position and n bar(x) elsewhere.

Usage

buildSSCP(sample.cov, sample.mean, sample.nobs)

Arguments

build the variance covariance point estimates model syntax

Description

build the variance covariance point estimates model syntax

Usage

buildVarCovSyntax(pt)

identify best scaling indicator

Description

identify best scaling indicator

Usage

chooseSI(model, data, scaling, lag = FALSE)

estimate the 2SLS point estimates

Description

estimate the 2SLS point estimates

Usage

est2SLSCoef(d = d, r = NULL, poly.mat = NULL, sscp.mat = NULL)

estimate the 2SLS coefficient covariance matrix

Description

estimate the 2SLS coefficient covariance matrix

Usage

est2SLSCoefCov(
  d,
  poly.mat = NULL,
  cov.mat = NULL,
  mean.vec = NULL,
  acov = NULL,
  acov.sat = NULL,
  r = NULL
)

estimate the 2SLS equation specific sigma squared

Description

estimate the 2SLS equation specific sigma squared

Usage

est2SLSSigmaSq(d, cov.mat)

Calculate the residual covariance matrix

Description

Calculate the residual covariance matrix

Usage

estResidualCov(d, sample.cov)

estimate the SEs using two-stage ML

Description

estimate the SEs using two-stage ML

Usage

estTwoStageML(g, v, eqns, pt)

estimate the variance and covariance parameters

Description

estimate the variance and covariance parameters

Usage

estVarCovarCoef(
  data,
  g,
  eqns,
  pt,
  ordered,
  vc.coef.estimator = "ML",
  vc.coef.missing = "FIML"
)

return a dataframe of parameter estimates for a fitted model.

Description

return a dataframe of parameter estimates for a fitted model.

Usage

estimatesTable(x, v = NULL, sarg = FALSE)

Arguments

provides factor scores for miiv model

Description

provides factor scores for miiv model

Usage

factorScores(model, data, lv_scores, lv_estimator)

Attractiveness and academic ability

Description

This data comes from a study by Felson and Borhnstedt (1979) of perceived attractiveness and academic ability in teenagers, sixth through ninth grade. The six variables are perception of academic ability (academic), perception of physical attractiveness (attract), grade point average (gpa), height, weight, and a strangers' rating of attractiveness (rating).

Usage

felson1979

Format

A data frame with 209 rows and 7 variables

Details

• acad.

• athl.

• attract.

• gpa.

• height.

• weight.

• rating.

References

Felson, R.B. & Bohrnstedt, G.W. (1979). "Are the good beautiful or the beautiful good?" The relationship between children's perceptions of ability and perceptions of physical attractiveness. Social Psychology Quarterly, 42, 386–392.

Examples

## Not run: 
  model <-  '
	 acad    ~ gpa + attract
    attract ~ height + weight + rating + acad
  '

## End(Not run)

fill the parameter table

Description

fill the parameter table

Usage

fillParTable(eqns, pt, v = NULL)

provides model lists for latent variable gimme

Description

provides model lists for latent variable gimme

Usage

getModelList(
  data,
  model,
  scaling = "first.indicator",
  lag = FALSE,
  dfm = FALSE
)

Model-implied instrumental variable (MIIV) estimation

Description

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

Usage

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 = "stepwise.R2"
)

Arguments

Details

• model

  The following model syntax operators are currently supported: =~, ~, ~~ and *. See below for details on default behavior, descriptions of how to specify the scaling indicator in latent variable models, and how to impose equality constraints on the parameter estimates.

  Example using Syntax Operators

  In the model below, 'L1 =~ Z1 + Z2 + Z3' indicates the latent variable L1 is measured by 3 indicators, Z1, Z2, and Z3. Likewise, L2 is measured by 3 indicators, Z4, Z5, and Z6. The statement 'L1 ~ L2' specifies latent variable L1 is regressed on latent variable L2. 'Z1 ~~ Z2' indicates the error of Z2 is allowed to covary with the error of Z3. The label LA3 appended to Z3 and Z6 in the measurement model constrains the factor loadings for Z3 and Z6 to equality. For additional details on constraints see Equality Constraints and Parameter Restrictions.

  model <- '
       L1 =~ Z1 + Z2 + LA3*Z3
       L2 =~ Z4 + Z5 + LA3*Z6
       L1  ~ L2
       Z2 ~~ Z3
    '

  Scaling Indicators

  Following the lavaan model syntax, latent variables are defined using the =~ operator. For first order factors, the scaling indicator chosen is the first observed variable on the RHS of an equation. For the model below Z1 would be chosen as the scaling indicator for L1 and Z4 would be chosen as the scaling indicator for L2.

  model <- '
       L1 =~ Z1 + Z2 + Z3
       L2 =~ Z4 + Z5 + Z6
    '

  Equality Constraints and Parameter Restrictions

  Within- and across-equation equality constraints on the factor loading and regression coefficients can be imposed directly in the model syntax. To specify equality constraints between different parameters equivalent labels should be prepended to the variable name using the * operator. For example, we could constrain the factor loadings for the two non-scaling indicators of L1 to equality using the following model syntax.

  model <- '
       L1 =~ Z1 + LA2*Z2 + LA2*Z3
       L2 =~ Z4 + Z5 + Z6
    '

  Researchers also can constrain the factor loading and regression coefficients to specific numeric values in a similar fashion. Below we constrain the regression coefficient of L1 on L2 to 1.

  model <- '
       L1 =~ Z1 + Z2 + Z3
       L2 =~ Z4 + Z5 + Z6
       L3 =~ Z7 + Z8 + Z9
       L1  ~ 1*L2 + L3
    '

  Higher-order Factor Models

  For example, in the model below, the scaling indicator for the higher-order factor H1 is taken to be Z1, the scaling indicator that would have been assigned to the first lower-order factor L1. The intercepts for lower-order latent variables are set to zero, by default

  model <- '
       H1 =~ L1 + L2 + L3
       L1 =~ Z1 + Z2 + Z3
       L2 =~ Z4 + Z5 + Z6
       L3 =~ Z7 + Z8 + Z9
    '

  Model Defaults

  In addition to those relationships specified in the model syntax MIIVsem will automatically include the intercepts of any observed or latent endogenous variable. The intercepts for any scaling indicators and lower-order latent variables are set to zero by default. Covariances among exogenous latent and observed variables are included when var.cov = TRUE. Where appropriate the covariances of the errors of latent and observed dependent variables are automatically included in the model specification. These defaults correspond to those used by lavaan and auto = TRUE, except that endogenous latent variable intercepts are estimated by default, and the intercepts of scaling indicators are fixed to zero.

  Invalid Specifications

  Certain model specifications are not currently supported. For example, the scaling indicator of a latent variable is not permitted to cross-load on another latent variable. In the model below Z1, the scaling indicator for L1, cross-loads on the latent variable L2. Executing a search on the model below will result in the warning: miivs: scaling indicators with a factor complexity greater than 1 are not currently supported.

  model <- '
      L1 =~ Z1 + Z2 + Z3
      L2 =~ Z4 + Z5 + Z6 + Z1
    '

  In addition, MIIVsem does not currently support relations where the scaling indicator of a latent variable is also the dependent variable in a regression equation. The model below would not be valid under the current algorithm.

  model <- '
      L1 =~ Z1 + Z2 + Z3
      Z1  ~ Z4
      Z4  ~ Z5 + Z6
    '

• instruments

  To utilize this option you must first define a list of instruments using the syntax displayed below. Here, the dependent variable for each equation is listed on the LHS of the ~ operator. In the case of latent variable equations, the dependent variable is the scaling indicator associated with that variable. The instruments are then given on the RHS, separated by + signs. The instrument syntax is then encloses in single quotes. For example,

  customIVs <- '
       y1 ~ z1 + z2 + z3
       y2 ~ z4 + z5
    '
    

  After this list is defined, set the instruments argument equal to the name of the list of instruments (e.g. customIVs). Note, that instruments are specified for an equation, and not for a specific endogenous variable. If only a subset of dependent variables are listed in the instruments argument, only those equations listed will be estimated. If external or auxiliary instruments (instruments not otherwise included in the model) are included the miiv.check argument should be set to FALSE.

• sample.cov

  The user may provide a sample covariance matrix in lieu of raw data. The rownames and colnames must contain the observed variable names indicated in the model syntax. If sample.cov is not NULL the user must also supply a vector of sample means (sample.mean), and the number of sample observations (sample.nobs) from which the means and covariances were calculated. If no vector of sample means is provided intercepts will not be estimated. MIIVsem does not support bootstrap standard errors or polychoric instrumental variable estimtation when the sample moments, rather than raw data, are used as input.

• sample.mean

  A vector of length corresponding to the row and column dimensions of the sample.cov matrix. The names of sample.mean must match those in the sample.cov. If the user supplies a covariance matrix but no vector of sample means intercepts will not be estimated.

• sample.cov.rescale

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

• estimator

  The default estimator is 2SLS. For equations with continuous variables only and no restrictions the estimates are identical to those described in Bollen (1996, 2001). If restrictions are present a restricted MIIV-2SLS estimator is implemented using methods similar to those described by Greene (2003) but adapted for moment based estimation. 2SLS coefficients and overidentifcation tests are constructed using the sample moments for increased computational efficiency.

  If an equation contains ordered categorical variables, declared in the ordered argument, the PIV estimator described by Bollen and Maydeu-Olivares (2007) is implemented. The PIV estimator does not currently support exogenous observed predictors of endogenous categorical variables. See details of the ordered argument for more information about the PIV estimator.

• se When se is set to "boot" or "bootstrap" standard errors are computed using a nonparametric bootstrap assuming an independent random sample. If var.cov = TRUE nonceonvergence may occur and any datasets with impproper solutions will be recorded as such and discarded. Bootstrapping is implemented using the boot by resampling the observations in data and refitting the model with the resampled data. The number of bootstrap replications is set using the bootstrap argument, the default is 1000. Here, the standard errors are based on the standard deviation of successful bootstrap replications. Note, the Sargan test statistic is calculated from the original sample and is not a bootstrap-based estimate. When se is set to "standard" standard errors for the MIIV-2SLS coefficients are calculated using analytic expressions. For equations with categorical endogenous variables, the asymptotic distribution of the coefficients is obtained via a first order expansion where the matrix of partial derivatives is evaluated at the sample polychoric correlations. For some details on these standard errors see Bollen & Maydeu-Olivares (2007, p. 315). If var.cov = TRUE only point estimates for the variance and covariance estimates are calculated. To obtain standard errors for the variance and covariance parameters we recommend setting se = "bootstrap". Analytic standard errors for the variance covariance parameters accounting for the first stage estimation have been derived and will be available in future releases.

• missing There are two ways to handle missing data in MIIVsem. First, missing data may be handled by listwise deletion (missing = "listwise"), In this case any row of data containing missing observation is excluded from the analysis and the sample moments are adjusted accordingly. Estimation then proceeds normally. The second option for handling missing data is through a two-stage procedures missing = "twostage" where consistent estimates of the saturated populations means and covariance are obtained in the first stage. These quantities are often referred to as the "EM means" and "EM covariance matrix." In the second stage the saturated estimates are used to calculate the MIIV-2SLS structural coefficients. Bootstrap standard errors are recommended but will be computationally burdensome due to the cost of calculating the EM-based moments at each bootstrap replication.

• ordered For equations containing ordered categorical variables MIIV-2SLS coefficients are estimated using the approach outlined in Bollen & Maydeu-Olivares (2007). The asymptotic distribution of the these coefficients is obtained via a first order expansion where the matrix of partial derivatives is evaluated at the sample polychoric correlations. For some details on these standard errors see Bollen & Maydeu-Olivares (2007, p. 315). If var.cov = TRUE only point estimates for the variance and covariance estimates are calculated using the DWLS estimator in lavaan. To obtain standard errors for the variance and covariance parameters we recommend the bootstrap approach. Analytic standard errors for the variance covariance parameters in the presence of endogenous categorical variables will be available in future releases. Currently MIIVsem does not support exogenous variables in equations with categorical endogenous variables.

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), 827–842.

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), 393–415.

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

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), 280–302.

See Also

MIIVsemmiivs

two-stage least square estimator for a system of equations

Description

two-stage least square estimator for a system of equations

Usage

miive.2sls(d, g, r, est.only, se, missing, var.cov, sarg.adjust = "none")

Arguments

Model-implied instrumental variable (MIIV) search

Description

A key step in the MIIV-2SLS approach is to transform the SEM by replacing the latent variables with their scaling indicators minus their errors. Upon substitution the SEM is transformed from a model with latent variables to one containing observed variables with composite errors. The miivs function automatically makes this transformation. The miivs function will also identify equation-specific model-implied instrumental variables in simultaneous equation models without latent variables.

Usage

miivs(model)

Arguments

Details

• model

  A model specified using the model syntax employed by lavaan. The following model syntax operators are currently supported: =~, ~, ~~ and *. See below for details on default behaviors, how to specify the scaling indicator in latent variable models, and how to impose equality constraints on the parameter estimates.

  Example using Syntax Operators

  In the model below, 'L1 =~ Z1 + Z2 + Z3' indicates the latent variable L1 is measured by 3 indicators, Z1, Z2, and Z3. Likewise, L2 is measured by 3 indicators, Z4, Z5, and Z6. The statement 'L1 ~ L2' specifies latent variable L1 is regressed on latent variable L2. 'Z1 ~~ Z2' indicates the error of Z2 is allowed to covary with the error of Z3. The label LA3 appended to Z3 and Z6 in the measurement model equations constrains the factor loadings for Z3 and Z6 to equality. For additional details on constraints see Equality Constraints and Parameter Restrictions.

  model <- '
       L1 =~ Z1 + Z2 + LA3*Z3
       L2 =~ Z4 + Z5 + LA3*Z6
       L1  ~ L2
       Z2 ~~ Z3
    '

  Scaling Indicators

  Following the lavaan model syntax, latent variables are defined using the =~ operator. For first order factors, the scaling indicator chosen is the first observed variable on the RHS of an equation. For the model below Z1 would be chosen as the scaling indicator for L1 and Z4 would be chosen as the scaling indicator for L2.

  model <- '
       L1 =~ Z1 + Z2 + Z3
       L2 =~ Z4 + Z5 + Z6
    '

  Equality Constraints and Parameter Restrictions

  Within- and across-equation equality constraints on the factor loading and regression coefficients can be imposed directly in the model syntax. To specify equality constraints between different parameters equivalent labels should be prepended to the variable name using the * operator. For example, we could constrain the factor loadings for two non-scaling indicators of latent factor L1 to equality using the following model syntax.

  model <- '
       L1 =~ Z1 + LA2*Z2 + LA2*Z3
       L2 =~ Z4 + Z5 + Z6
    '

  Researchers can also constrain the factor loadings and regression coefficients to specific numeric values in a similar fashion. Below we constrain the regression coefficient of L1 on L2 to 1.

  model <- '
       L1 =~ Z1 + Z2 + Z3
       L2 =~ Z4 + Z5 + Z6
       L3 =~ Z7 + Z8 + Z9
       L1  ~ 1*L2 + L3
    '

  Higher-order Factor Models

  For example, in the model below, the scaling indicator for the higher-order factor H1 is taken to be Z1, the scaling indicator that would have been assigned to the first lower-order factor L1. The intercepts for lower-order latent variables are set to zero, by default

  model <- '
       H1 =~ L1 + L2 + L3
       L1 =~ Z1 + Z2 + Z3
       L2 =~ Z4 + Z5 + Z6
       L3 =~ Z7 + Z8 + Z9
    '

  Model Defaults

  In addition to those relationships specified in the model syntax MIIVsem will automatically include the intercepts of any observed or latent endogenous variable. The intercepts for any scaling indicators and lower-order latent variables are set to zero. Covariances among exogenous latent and observed variables are included by default when var.cov = TRUE. Where appropriate the covariances of the errors of latent and observed dependent variables are also automatically included in the model specification. These defaults correspond to those used by lavaan and auto = TRUE, except that endogenous latent variable intercepts are estimated by default, and the intercepts of scaling indicators are fixed to zero.

  Invalid Specifications

  Certain model specifications are not currently supported. For example, the scaling indicator of a latent variable is not permitted to cross-load on another latent variable. In the model below Z1, the scaling indicator for L1, cross-loads on the latent variable L2. Executing a search on the model below will result in the warning: miivs: scaling indicators with a factor complexity greater than 1 are not currently supported.

  model <- '
      L1 =~ Z1 + Z2 + Z3
      L2 =~ Z4 + Z5 + Z6 + Z1
    '

  In addition, MIIVsem does not currently support relations where the scaling indicator of a latent variable is also the dependent variable in a regression equation. For example, the model below would not be valid under the current algorithm.

  model <- '
      L1 =~ Z1 + Z2 + Z3
      Z1  ~ Z4
      Z4  ~ Z5 + Z6
    '

The miivs function displays a table containing the following information for each equation in the system:

• LHS The "dependent" variable.

• RHS The right hand side variables of the transformed equation.

• MIIVs The model-implied instrumental variables for each equation.

Value

A list of model equations.

References

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

Bentler, P. M., and Weeks, D. G. (1980). Linear Structural Equations with Latent Variables. Psychometrika, 45, 289–308.

See Also

miive

Parse user-implied instrumental variables

Description

Parse user-implied instrumental variables

Usage

parseInstrumentSyntax(d, instruments, miiv.check)

Print method for a MIIV estimation object

Description

Print method for a MIIV estimation object

Usage

## S3 method for class 'miive'
print(x, ...)

Arguments

Print method for a MIIV search object

Description

Print method for a MIIV search object

Usage

## S3 method for class 'miivs'
print(x, ...)

Arguments

Process data.

Description

Process data.

Usage

processData(
  data = data,
  sample.cov = sample.cov,
  sample.mean = sample.mean,
  sample.nobs = sample.nobs,
  ordered = ordered,
  missing = missing,
  se = se,
  pt = pt
)

Prune MIIVs based on some specified criterion.

Description

Prune MIIVs based on some specified criterion.

Usage

pruneExcessMIIVs(
  d,
  overid.degree,
  overid.method,
  data = NULL,
  sample.cov = NULL,
  sample.polychoric = NULL,
  sample.mean = NULL,
  sample.nobs = NULL,
  overid.boot = FALSE,
  cat.vars = NULL
)

Reisenzein data

Description

This dataset comes from Reisenzein (1986). In this paper Reisenzein designed a randomized experiment to test Weiner's attribution-affect model of helping behavior. According to this theory, whether people help others is determined by their anger or sympathy. Anger and sympathy are affected by perceived controllability. If the individuals have gotten into difficult situations as a result of their own controllable actions, then this negatively affects sympathy and positively affects anger of the potential helpers. The opposite holds if the situation seems beyond the individuals’ control. This data comes from an experiment that describes a person collapsing and lying on the floor of a subway. Subjects were told that the person was either drunk (controllable situation) or ill (uncontrollable situation). This randomized story was intended to affect perceptions of controllability, and controllability in turn affected feelings of sympathy and anger. Finally, sympathy should positively affect helping behavior while anger would negatively affect helping.

Usage

reisenzein1986

Format

A data frame with 138 rows and 13 variables

Details

• Z1. Eliciting Situation

• Z2. How controllable, do you think, is the cause of the person's present condition? (1 = not at all under personal control, 9 = completely under personal control).

• Z3. How responsible, do you think, is that person for his present condition? (1 = not at all responsible, 9 = very much responsible).

• Z4. I would think that it was the person's own fault that he is in the present situation. (1 = no. not at all. 9 = yes, absolutely so).

• Z5. How much sympathy would you feel for that person? (1 = none at all. 9 = very much).

• Z6. I would feel pity for this person. (1 = none at all, 9 = very much).

• Z7. How much concern would you feel for this person? (1 = none al all, 9 = very much).

• Z8. How angry would you feel at that person? (1 = not at all, 9 = very much).

• Z9. How irritated would you feel by that person? (1 = not at all, 9 = very much).

• Z10. I would feel aggravated by that person. (1 = not at all, 9 = very much so).

• Z11. How likely is it that you would help that person? (1 = definitely would not help. 9 = definitely would help).

• Z12. How certain would you feel that you would help the person? (1 = not at all certain. 9 = absolutely certain).

• Z13. Which of the following actions would you most likely engage in? 1 = not help at all; 2 = try to alert other bystanders, but stay uninvolved myself; 3 = try to inform the conductor or another official in charge; 4 = go over and help the person to a seat; 5 = help in any way that might be necessary, including if necessary first aid and/or accompanying the person to a hospital.

References

Reisenzein, R. (1986). A Structural Equation Analysis of Weiner's Attribution-Affect Model of Helping Behavior. Journal of Personality and Social Psychology, 50(6), 1123–33.

Summary information for a MIIV estimation object

Description

Summary information for a MIIV estimation object

Usage

## S3 method for class 'miive'
summary(object, eq.info = FALSE, restrict.tests = FALSE, rsquare = FALSE, ...)

Arguments

References

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

Henningsen, A., and Hamann, J.D. (2007). systemfit: A Package for Estimating Systems of Simultaneous Equations in R. Journal of Statistical Software 23(4), 1-40.

Summary information for a MIIV search object

Description

Summary information for a MIIV search object

Usage

## S3 method for class 'miivs'
summary(object, miivs.out = FALSE, eq.info = FALSE, ...)

Arguments