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I am reviewing the R package OpenMx for a genetic epidemiology analysis in order to learn how to specify and fit SEM models. I am new to this so bear with me. I am following the example on page 59 of the OpenMx User Guide. Here they draw the following conceptual model:

SEM models for identical & fraternal twins

And in specifying the paths, they set the weight of the latent "one" node to the manifested bmi nodes "T1" and "T2" to be 0.6 because:

The main paths of interest are those from each of the latent variables to the respective observed variable. These are also estimated (thus all are set free), get a start value of 0.6 and appropriate labels.

# path coefficients for twin 1
mxPath(
  from=c("A1","C1","E1"),
  to="bmi1",
  arrows=1,
  free=TRUE,
  values=0.6,
  label=c("a","c","e")
),

# path coefficients for twin 2
mxPath(
  from=c("A2","C2","E2"),
  to="bmi2",
  arrows=1,
  free=TRUE,
  values=0.6,
  label=c("a","c","e")
),

The value of 0.6 comes from the estimated covariance of bmi1 and bmi2 (of strictly monozygotic twin pairs). I have two questions:

  1. When they say that the path is given a "starting" value of 0.6 is this like setting a numerical integration routine with initial values, like in estimation of GLMs?

  2. Why is this value estimated strictly from the monozygotic twins?

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To answer your 2 points:

1) Yes, exactly--the starting value is merely dictating where the algorithm will start the optimization process. Most software packages actually determine their own starting value by default, and the user needs to try inputting different values only when problems occur during estimation. From my experience, most plausible starting values will do, and will not change the final model on which the algorithm converges.

2) The value 0.6 is the starting value not for the intercept of T1 and T2 (path between "one" and T1 & T2), but it is instead the starting value for the factor loadings linking each latent variable (A, C, E) to their indicator T1 or T2. This is indicated by the fact that the path goes from=c("A1","C1","E1"), to="bmi1" in the first case, and from=c("A2","C2","E2"), to="bmi2" in the second case.

As for the specific value "0.6": I could not find in the documentation where they mention taking this value based on the monozygotic twins subgroup; and actually, these parameter estimates (factor loadings for the 3 latent variables) cannot be directly computed from the sample, since by definition, these latent variables are unobserved (they are latent). As I mention in point #1, rarely will the choice between two plausible values affect the parameter estimates of the converged model, so my guess is that they simply chose one of many plausible values for these factor loadings as starting values. Whether this value does come from the estimated covariance between bmi1 and bmi2 in the monozygotic-twin subgroup only should be irrelevant, since any plausible starting values should lead the algorithm to converge upon the same final values, perhaps with some differences in computation time. (And my advice to convince yourself is: try it! Try several starting values and compare the parameter estimates of the converged models.)

As a general note, I will point out that the choice of starting values for any parameter estimate becomes VERY important if the argument free is set to FALSE, because the starting value will effectively become the value of the parameter estimate in the final model (it will not be estimated; it is fixed before estimation).

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