umx (version 4.9.0)

umxMendelianRandomization: Build a SEM implementing the equivalent of 2-stage least squares regression

Description

umxTwoStage implementing the Structural Equation Model equivalent of a 2SLS regression. For ease of learning, the function is modeled closely on the sem::tsls().

Usage

umxMendelianRandomization(
  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)

Value

• mxModel()

Details

The example is a Mendelian Randomization analysis showing the utility of SEM over two-stage regression.

The following figure shows how the ACE model appears as a path diagram:

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

• umx_make_MR_data(), sem::tsls(), umxRAM()

Other Super-easy helpers: umxEFA(), umx

Examples

# NOT RUN {
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 = umxTwoStage(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 = umxMendelianRandomization(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))
# }