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From |
"Cathy L. Antonakos" <cathya@umich.edu> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: working with a vector and scalars |

Date |
Mon, 9 Jun 2008 19:48:09 -0400 (EDT) |

Here's a solution to my question about working with vectors and scalars. Thank you, Austin Nichols, for providing initial code and a hint about difficulty generating element-wise reciprocals.

I initially had a problem using the "placeXhr" variable in the -mean- command, because "placeXhr" is a string variable. That problem is solved by using both "place" and "hour" variables in -mean-.

The reliabilities in the sub-groups turned out to be very similar.

Cathy

----

*Calculate reliabilities for place/hour groups.

egen N = count(crowdindx), by(place hour)

gen nr=1/N

mean nr, over(place hour)

mat b=e(b)

mat N=b'

matrix rownames N = `e(over_labels)'

loneway crowdindx placeXhr

matrix sj = N * (r(sd_w) * r(sd_w)) local tau = r(sd_b) * r(sd_b) matrix t = J(48,1,`tau') matrix J = t,sj matrix rownames J = `e(over_labels)'

matrix colnames J = tau sigma_nj

preserve

drop _all

svmat J, names(col)

tempfile mat

save `mat'

use `mat'

gen lambda_j = tau / (tau + sigma_nj)

restore

*End of reliability analysis.

On Mon, 9 Jun 2008, Cathy L. Antonakos wrote:

Date: Mon, 9 Jun 2008 08:52:07 -0400 (EDT)

From: Cathy L. Antonakos <cathya@umich.edu>

Reply-To: statalist@hsphsun2.harvard.edu

To: statalist@hsphsun2.harvard.edu

Subject: Re: st: working with a vector and scalars

You're right. The "d" in the equation should be "s" (sigma-squared). I can get the reliability reported by -loneway- for the overall sample mean, but I want the reliabilities for each group.

Yes, I think it would be easier in Mata, but I don't know how to do that.

When I ran the syntax you provided, the -mean- command gave an error:

. mean nr, over(placeXhr)

no observations

r(2000);

If I can figure out that error, I think the approach will work.

On Sun, 8 Jun 2008, Austin Nichols wrote:

Date: Sun, 8 Jun 2008 21:00:38 -0400

From: Austin Nichols <austinnichols@gmail.com>

Reply-To: statalist@hsphsun2.harvard.edu

To: statalist@hsphsun2.harvard.edu

Subject: Re: st: working with a vector and scalars

Cathy L. Antonakos <cathya@umich.edu>

I take it you don't want the reliability reported by -loneway-? Not

sure what you want from your description... but I don't think that

equation looks right, and I don't have the ref handy. Can you confirm

that t cancels out? Is your calculated s equiv to d in your formula?

I don't see where you've tried to calculate something and gotten an

error, but try:

egen N = count(crowdindx), by(placeXhr)

g nr=1/N

mean nr, over(placeXhr)

mat b=e(b)

mat N=b'

loneway crowdindx placeXhr

scalar t = r(sd_b) * r(sd_b)

scalar s = r(sd_w) * r(sd_w)

mat lambda = s*N

mat li lamdba

But if you need to calculate the element-wise reciprocal, it's easier in Mata...

On Sun, Jun 8, 2008 at 8:23 PM, Cathy L. Antonakos <cathya@umich.edu> wrote:

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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**References**:**st: working with a vector and scalars***From:*"Cathy L. Antonakos" <cathya@umich.edu>

**Re: st: working with a vector and scalars***From:*"Austin Nichols" <austinnichols@gmail.com>

**Re: st: working with a vector and scalars***From:*"Cathy L. Antonakos" <cathya@umich.edu>

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