# Model Implied Instrumental Variable (MIIV) Estimation of Structural Equation Models

Functions for estimating structural equation models using instrumental variables.

MIIVsem is an R package for estimating structural equation models using model-implied instrumental variables.

Version 0.5.2 includes the following features:

• Estimation of latent variable and simultaneous equation models.
• Model-implied and traditional instrumental variable estimation.
• Equation level specification tests.
• Efficient computation from covariance matrix input.
• Polychoric instrumental variable estimation for endogenous categorical variables.
• Impose and test within- and across-equation parameter restrictions.
• Bootstrap standard errors.
• Variance and covariance parameter estimation.

### Installation

In R you can install MIIVsem from CRAN as follows:

### Usage

MIIVsem uses a subset of the model syntax employed by lavaan (Rosseel, 2012) for model specification. The following model syntax operators are currently supported:

Operators
=~ Used for expressing measurement relations, read as 'measured by.'
~ Used For expressing regression relations, read as 'regressed on.'
~~ For specifying variances and covariances, read as 'covaries with.'
* For assigning equality or numerical constraints.

### Model Syntax

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` prepended to `Z3` and `Z6` in the measurement model equations constrains the factor loadings for `Z3` and `Z6` to equality.

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`.

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.

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`.

Higher Order Factor Model

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 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. Where appropriate the covariances of the errors of latent and observed dependent variables are also 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.

### Getting Started

MIIV Search

Researchers typically search for instrumental variables external to the model. The key property of valid instruments is that they are uncorrelated with equation error. The MIIV approach proposed in Bollen (1996) finds instruments among observed variables already in the model. Here, the model specification itself implies which observed variables are uncorrelated with the equation disturbance.

Using the industrialization-democracy example from Bollen (1989) we illustrate the MIIV Search:

MIIV-2SLS Estimation

We can also estimate the industrialization-democracy model using MIIV-2SLS:

Estimation from Sample Moments

Bootstrap Standard Errors (Version 0.5.2)

Categorical Endogenous Variables (Bollen & Maydeu-Olivares (2007))

### Replication of Textbook Results

Following Henningsen and Hamann (2007) we replicate textbook results from

Klein's Model I (Greene, 2003, p.381)

# Reference manual

install.packages("MIIVsem")

0.5.2 by Zachary Fisher, 9 months ago

https://github.com/zackfisher/MIIVsem

Report a bug at https://github.com/zackfisher/MIIVsem/issues

Browse source code at https://github.com/cran/MIIVsem

Authors: Zachary Fisher [aut, cre], Keneth Bollen [aut], Kathleen Gates [aut], Mikko Rönkkö [aut]

Documentation:   PDF Manual

Task views: Psychometric Models and Methods