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From |
David Airey <david.airey@vanderbilt.edu> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: xtmixed syntax |

Date |
Thu, 22 May 2008 22:11:13 -0500 |

.

Thank you very much for this level of detail, Yulia. This is a terrific explanation. I now have your article too. I was far from the last syntax, but now with your explanations, I might be able to figure out similar syntax de novo. I will try out both approaches and report back (another person is tackling the same model with SAS Proc Mixed) so it will make a good comparison.

-Dave

On May 22, 2008, at 2:51 PM, ymarchenko@stata.com wrote:

David Airey <david.airey@vanderbilt.edu> asks about how to obtain variance

components by using -xtmixed- for an experimental design with both nested and

crossed factors:

Before demonstrating the actual syntax of -xtmixed- for David's example, letI have a variance components mixed model that I am have trouble with syntax using xtmixed. I'm interested in a genetic polymorphism effect (think of this as simple treatment effect) on gene expression, where gene expression is measured on set of genes where genes are actually measured by multiple probes. two group allelic fixed effect A random sample effect S, one sample per subject, subjects nested in allelic group, 80 subjects random gene effect G, measured on all samples, so crossed with group, typically 20-50 genes random probe effect P, nested in gene, < 5 probes per gene, different probes per gene ...

me first briefly discuss a more general idea behind using -xtmixed- with

random-effects experimental designs. A more detailed discussion is given in

Marchenko (2006) (in fact, David's example is similar to the example described

in section 4.6 of the article).

There are several ways of using -xtmixed- to obtain variance components from a

random-effects experimental design. One is what we call the brute- force way

of fitting the design. It is straightforward. There are also other

alternative ways of obtaining the same results. These approaches are more

efficient in terms of memory usage and speed but require using the alternate

formulation of the design as a multilevel model that may be difficult to find

for certain designs.

With the brute-force way (or design-matrix-based approach), the first step is

to construct the design matrix for random effects, corresponding to the

design. Such a random-effects design matrix will be comprised of columns

containing indicator variables corresponding to the levels of all random

effects. -xtmixed- accommodates the specification of this matrix via the

special group identifier -_all- and the factor notation - R._varname_- (see

[XT] xtmixed for details). Thus, all we need to do prior to using - xtmixed-

is to identify all random effects (or, equivalently, all variance components)

associated with the design.

Returning to David's example, probes are nested within genes, and groups are

crossed with genes and probes. Since the group effect is fixed, we have the

following variance components for this design: variability due to genes,

variability due to probes (nested within genes), variability due to the

interaction of groups and genes, variability due to the interaction of groups

with probes (nested within genes), and subject variability (residual

variance). Our four random effects are genes, probes (nested within genes),

group-gene interaction, and group-probe-(nested-within-genes) interaction.

Note that when a fixed factor is interacted with a random factor, the

interaction term is random.

Suppose that variables Group, Gene, and Probe contain information about

groups, genes, and probes, respectively. For this design, we also need to

create the following interaction terms:

. egen GeXPr = group(Gene Probe)

. egen GrXGe = group(Group Gene)

. egen GrXGeXPr = group(Group Gene Probe)

Now, the brute-force way of using -xtmixed- for this design is

straightforward: we simply list all of the random-effects variables as

separate equations using the -_all: R._varname_- notation. The corresponding

syntax is:

. xi: xtmixed depvar i.Group || _all: R.Gene || _all: R.GeXPr || _all: R.GrXGe ///

|| _all: R.GrXGeXPr, variance

In the above syntax, -_all: R.Gene-, for example, tells -xtmixed- to include

indicators corresponding to levels of variable Gene into the design matrix.

The variability within subjects (the lowest-level variability) is estimated by

the residual variance, reported by -xtmixed-.

The advantage of the brute-force way is that it is straightforward once the

relevant random-effects terms are identified. However, for David's example,

the above syntax requires creating a matrix with 50+50*5+2*50+2*50*5 = 900

columns (50 is the number of genes, 5 is the number of probes, and 2 is the

number of groups). We can avoid this by using the more efficient way of

obtaining the same results by using an alternative syntax of - xtmixed-.

First, consider the terms Gene, GrXGe, and GrXGeXPr. Since interaction terms

can be viewed as nested terms, we can obtain variance components for these

three terms more efficiently from a three-level model with genes defining the

first level, groups defining the second level, and probes defining the third

level. The corresponding syntax of -xtmixed- is

. xi: xtmixed depvar i.Group || Gene: || Group: || Probes:, variance

What we did not take into account in the above syntax is the fact that probes

are nested within genes. As described in example 7 of [XT] xtmixed and

section 4.4 of the cited article, the nesting can be accommodated by viewing

the levels of the nested effects (Probes) as random coefficients for nesting

level (Genes) and specifying the exchangeable covariance structure for these

random coefficients. Taking this into account, the final syntax for -xtmixed-

is

. xi: xtmixed depvar i.Group || Gene: R.Probes, cov(exchangeable) ///

|| Group: || Probes:, variance

By using the above syntax, we also significantly reduced the column dimension

of the design matrix (from 900 in the brute-force method to 5+1+1=7).

Reference:

Marchenko, Y. 2006. Estimating variance components in Stata. The Stata

Journal, 6(1): 1-22.

The link to the article is

http://www.stata-journal.com/article.html?article=st0095

-- Yulia

ymarchenko@stata.com

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**Follow-Ups**:**RE: st: xtmixed syntax [anova]***From:*"Feiveson, Alan H. (JSC-SK311)" <alan.h.feiveson@nasa.gov>

**References**:**Re: st: xtmixed syntax***From:*ymarchenko@stata.com

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