umxTwoStage
Build a SEM implementing the equivalent of 2-stage least squares regression
Description
umxMR (umxTwoStage) implements the Structural Equation Model equivalent of a 2SLS regression.
For ease of learning, the parameters follow the tsls() function in the sem package.
Usage
umxTwoStage( formula = Y ~ X, instruments = ~qtl, data, subset, weights, contrasts = NULL, name = "tsls", ... )
Arguments
formula |
The structural equation to be estimated (default = Y ~ X). A constant is implied if not explicitly deleted. |
instruments |
A one-sided formula specifying instrumental variables (default = qtl). |
data |
Frame containing the variables in the model. |
subset |
(optional) vector specifying a subset of observations to be used in fitting the model. |
weights |
(optional) vector of weights to be used in the fitting process (not supported) If specified should be a non-negative numeric vector with one entry for each observation, to be used to compute weighted 2SLS estimates. |
contrasts |
an optional list (not supported) |
name |
for the model (default = "tsls") |
... |
arguments to be passed along. (not supported) |
Details
The example is a Mendelian Randomization analysis showing the utility of SEM over two-stage regression.
The following figure shows how the MR model appears as a path diagram:
Value
References
-
-
Fox, J. (1979) Simultaneous equation models and two-stage least-squares. In Schuessler, K. F. (ed.) Sociological Methodology, Jossey-Bass.
-
-
Greene, W. H. (1993) Econometric Analysis, Second Edition, Macmillan.
See Also
Examples
library(umx) # ==================================== # = Mendelian Randomization analysis = # ==================================== ## Not run: # Note: in practice: many more subjects are desirable - this just to let example run fast df = umx_make_MR_data(1000) m1 = umxMR(Y ~ X, instruments = ~ qtl, data = df) parameters(m1) plot(m1, means = FALSE, min="") # help DiagrammaR layout the plot. m2 = umxModify(m1, "qtl_to_X", comparison=TRUE, tryHard="yes", name="QTL_affects_X") # yip m3 = umxModify(m1, "X_to_Y" , comparison=TRUE, tryHard="yes", name="X_affects_Y") # nope plot(m3, means = FALSE) # Errant analysis using ordinary least squares regression (WARNING this result is CONFOUNDED!!) m1 = lm(Y ~ X , data = df); coef(m1) # incorrect .35 effect of X on Y m1 = lm(Y ~ X + U, data = df); coef(m1) # Controlling U reveals the true 0.1 beta weight df = umx_make_MR_data(1e5) m1 = umxMR(Y ~ X, instruments = ~ qtl, data = df) coef(m1) # ====================== # = Now with sem::tsls = # ====================== # library(sem) # may require you to install X11 m2 = sem::tsls(formula = Y ~ X, instruments = ~ qtl, data = df) coef(m2) # Try with missing value for one subject: A benefit of the FIML approach in OpenMx. m3 = tsls(formula = Y ~ X, instruments = ~ qtl, data = (df[1, "qtl"] = NA)) ## End(Not run)