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st: working with a vector and scalars


From   "Cathy L. Antonakos" <cathya@umich.edu>
To   statalist@hsphsun2.harvard.edu
Subject   st: working with a vector and scalars
Date   Sun, 8 Jun 2008 20:23:23 -0400 (EDT)

I am working with scalars and a vector to estimate sample mean reliability by group, using a formula from Bryk & Raudenbush (1992) Hierarchical Linear Models:

lambda-j = t / [ t / (d /Nj)]

lambda-j is the reliability estimate for group j, t is between-group variance, d is within-group variance, and Nj is the group N.

Nj is a vector. The other parameters (t, d) are scalars.

Here's what I tried using -matrix- and -scalar-. The vector comes from a collapsed dataset. The scalars come from -loneway- using the original (uncollapsed) dataset. I have no trouble producing the vector and scalars, but can't figure out how to get them into the same matrix or file together so I can calculate the reliability esimates.

Any help will be much appreciated.

Cathy Antonakos

--------------
. bys placeXhr: egen N = count(crowdindx)
. preserve
. collapse (max) N, by(placeXhr)
. mkmat N
. levelsof placeXhr, local(l)
. matrix rownames N = `l' . matrix list N

N[49,1]
N
2_10 2
2_11 81
2_12 150
2_13 340
2_14 138
2_15 82
2_16 102
2_17 119
2_18 288
2_19 160
2_8 48
2_9 265
3_10 166
3_11 71
3_12 63
3_13 25
3_14 53
3_15 68
3_16 44
3_17 61
3_18 33
3_19 35
3_8 36
3_9 16
6_10 33
6_11 69
6_12 82
6_13 30
6_14 87
6_15 90
6_16 90
6_17 92
6_18 63
6_19 79
6_8 86
6_9 41
9_10 57
9_11 135
9_12 113
9_13 83
9_14 152
9_15 168
9_16 160
9_17 151
9_18 97
9_19 147
9_8 216
9_9 166
9_9 190

. restore

. *create matrices from -loneway- parameter estimates.
. preserve
. loneway crowdindx placeXhr

One-way Analysis of Variance for crowdindx: Crowding Index (wtd. sum)

Number of obs = 5121
R-squared = 0.5384

Source SS df MS F Prob > F
-------------------------------------------------------------------------
Between placeXhr 682650.69 47 14524.483 125.87 0.0000
Within placeXhr 585364.53 5073 115.38824
-------------------------------------------------------------------------
Total 1268015.2 5120 247.65922

Intraclass Asy.
correlation S.E. [95% Conf. Interval]
------------------------------------------------
0.54152 0.06135 0.42126 0.66177

Estimated SD of placeXhr effect 11.67412
Estimated SD within placeXhr 10.74189
Est. reliability of a placeXhr mean 0.99206
(evaluated at n=105.73)

. return list

scalars:
r(lb) = .4212643949911408
r(ub) = .6617675540515819
r(se) = .0613539740927638
r(sd_w) = 10.74189173110937
r(sd_b) = 11.67412402231762
r(rho_t) = .9920556043556278
r(rho) = .5415159745213614
r(N) = 5121

. scalar t = r(sd_b) * r(sd_b) . scalar s = r(sd_w) * r(sd_w)
. restore

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