| Title: | Model Implied Instrumental Variable (MIIV) Estimation of Structural Equation Models |
|---|---|
| Description: | Functions for estimating structural equation models using instrumental variables. |
| Authors: | Zachary Fisher [aut, cre], Kenneth Bollen [aut], Kathleen Gates [aut], Mikko Rönkkö [aut] |
| Maintainer: | Zachary Fisher <[email protected]> |
| License: | GPL-2 |
| Version: | 0.5.8 |
| Built: | 2024-11-04 03:03:20 UTC |
| Source: | https://github.com/zackfisher/miivsem |
MIIVsem is a package for estimating structural equation models using model-implied instrumental variables (MIIVs).
Maintainer: Zachary Fisher [email protected]
Authors:
Kenneth Bollen
Kathleen Gates
Mikko Rönkkö
Useful links:
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:
bollen1989abollen1989a
A data frame with 75 rows and 9 variables
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
Bollen, K. A. (1989). Structural equation models. New York: Wiley-Interscience.
## 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)## 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)
A dataset from McDonald and Clelland (1984) reanalyzed by Bollen (1989) containing data on union sentiment of southern nonunion textile workers.
bollen1989bbollen1989b
A data frame with 173 rows and 5 variables
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
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.
## Not run: model <- ' unionsen ~ deferenc + laboract + yrsmill deferenc ~ age laboract ~ age + deferenc yrsmill ~~ age ' ## End(Not run)## Not run: model <- ' unionsen ~ deferenc + laboract + yrsmill deferenc ~ age laboract ~ age + deferenc yrsmill ~~ age ' ## End(Not run)
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).
bollen1989cbollen1989c
A data frame with 432 rows and 5 variables
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
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.
## Not run: model <- ' subinc ~ inc + subocc subocc ~ occ + subinc subgen ~ subinc + subocc subinc ~~ subocc + subgen subocc ~~ subgen inc ~~ occ ' ## End(Not run)## Not run: model <- ' subinc ~ inc + subocc subocc ~ occ + subinc subgen ~ subinc + subocc subinc ~~ subocc + subgen subocc ~~ subgen inc ~~ occ ' ## End(Not run)
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.
bollen1996bollen1996
A data frame with 220 rows and 12 variables
access1.
access2.
access3.
access4.
access5.
access6.
easy1.
easy2.
easy3.
easy4.
easy5.
easy6.
Bollen, K. A., Speizer, I. S., & Mroz, T. A. (1996). Family Planning Facilities in Rural Tanzania: His and Her Perceptions of Time and Distance.
## Not run: model <- ' femaleAccess =~ access1 + access2 + access3 maleAccess =~ access4 + access5 + access6 femaleEasy =~ easy1 + easy2 + easy3 maleEasy =~ easy4 + easy5 + easy6 ' ## End(Not run)## Not run: model <- ' femaleAccess =~ access1 + access2 + access3 maleAccess =~ access4 + access5 + access6 femaleEasy =~ easy1 + easy2 + easy3 maleEasy =~ easy4 + easy5 + easy6 ' ## End(Not run)
return a dataframe of parameter estimates for a fitted model.
estimatesTable(x, v = NULL, sarg = FALSE)estimatesTable(x, v = NULL, sarg = FALSE)
x |
An object of class miive |
v |
A list containing variance snd covariance parameter information. |
sarg |
Logical. Should Sargan test results be included. |
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).
felson1979felson1979
A data frame with 209 rows and 7 variables
acad.
athl.
attract.
gpa.
height.
weight.
rating.
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.
## Not run: model <- ' acad ~ gpa + attract attract ~ height + weight + rating + acad ' ## End(Not run)## Not run: model <- ' acad ~ gpa + attract attract ~ height + weight + rating + acad ' ## End(Not run)
Estimate structural equation models using model-implied instrumental variables (MIIVs).
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" )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" )
model |
A model specified using lavaan model syntax or a
|
data |
A data frame, list or environment or an object coercible
by |
instruments |
This allows user to specify the instruments for
each equation. See Details and the |
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.nobs |
Number of observations in the full data frame. |
sample.cov.rescale |
If |
estimator |
Options |
se |
If "standard", asymptotic standard errors are
computed. If |
bootstrap |
Number of bootstrap draws, if bootstrapping is used. The
default is |
boot.ci |
Method for calculating bootstrap confidence intervals.
Options are normal approximation ( |
missing |
Default is |
est.only |
If |
var.cov |
If |
miiv.check |
Default is |
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 |
sarg.adjust |
Adjusment methods used to adjust the p-values associated
with the Sargan test due to multiple comparisons. Defaults is
|
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 |
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.
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.
MIIVsemmiivs
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.
miivs(model)miivs(model)
model |
A model specified using lavaan model syntax. See the
|
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.
A list of model equations.
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.
Print method for a MIIV estimation object
## S3 method for class 'miive' print(x, ...)## S3 method for class 'miive' print(x, ...)
x |
a miive object |
... |
Optional arguments to print, not used by user. |
Print method for a MIIV search object
## S3 method for class 'miivs' print(x, ...)## S3 method for class 'miivs' print(x, ...)
x |
a miivs object |
... |
Optional arguments to print, not used by user. |
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.
reisenzein1986reisenzein1986
A data frame with 138 rows and 13 variables
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.
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
## S3 method for class 'miive' summary(object, eq.info = FALSE, restrict.tests = FALSE, rsquare = FALSE, ...)## S3 method for class 'miive' summary(object, eq.info = FALSE, restrict.tests = FALSE, rsquare = FALSE, ...)
object |
An object of class |
eq.info |
A logical indicating whether equation-specific information should be printed. Useful in models with large numbers of variables. |
restrict.tests |
A logical indicating whether two test statistics for a large-sample wald test of linaer hypotheses imposed on the MIIV-2SLS coefficient matrix should be provided. The first statistic is an approximate F and the second is Chi-square. Assumptions and additional details for each test are given by Greene (2000, p. 346-347) and Henningsen and Hamman (2007). |
rsquare |
A logical indicating whether R-square values for
endogeneous variables are included in the output. Only
available when |
... |
Optional arguments to summary, not used by user. |
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
## S3 method for class 'miivs' summary(object, miivs.out = FALSE, eq.info = FALSE, ...)## S3 method for class 'miivs' summary(object, miivs.out = FALSE, eq.info = FALSE, ...)
object |
An object of class |
miivs.out |
A logical indicating whether the model-implied
instrumental variables found for |
eq.info |
A logical indicating whether equation-specific information should be printed. Useful in models with a large number of variables. |
... |
Optional arguments to summary, not used by user. |