Raykov composite reliability in stata?

[Senor Massao]

Hi,

I estimated the cronbach alpha as a measure of reliability for a scale using the following commands:

alpha x1 x2 x3 x4 x5 x6 x7 x8 x9 x10, std item

However, a reviewer asked to report the raykov composite reliability instead.

Any ideas how to do that in stata?

Any suggestion is highly appreciated.

Best wishes,
Massao

[Joseph Coveney]

Well, using the first example in this document by Tenko Raykov, you'd do something like that below.

.ÿversionÿ14.1

.ÿ
.ÿclearÿ*

.ÿsetÿmoreÿoff

.ÿ
.ÿquietlyÿssdÿinitÿy1ÿy2ÿy3ÿy4ÿy5

.ÿquietlyÿssdÿsetÿobservationsÿ300

.ÿquietlyÿssdÿsetÿcovarianceÿ1.322ÿ\ÿ0.878ÿ1.241ÿ\ÿ0.912ÿ0.886ÿ1.313ÿ\ÿ///
>ÿÿÿÿÿÿÿÿÿ0.858ÿ0.807ÿ0.881ÿ1.240ÿ\ÿ2.670ÿ2.567ÿ2.668ÿ2.560ÿ8.243

.ÿ
.ÿsemÿ(y1-y5ÿ<-ÿF),ÿvariance(F@1)ÿnocnsreportÿnodescribeÿnolog

StructuralÿequationÿmodelÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿNumberÿofÿobsÿÿÿÿÿ=ÿÿÿÿÿÿÿÿ300
Estimationÿmethodÿÿ=ÿml
Logÿlikelihoodÿÿÿÿÿ=ÿ-1954.2738

------------------------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿÿÿÿÿ|ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿOIM
ÿÿÿÿÿÿÿÿÿÿÿÿÿ|ÿÿÿÿÿÿCoef.ÿÿÿStd.ÿErr.ÿÿÿÿÿÿzÿÿÿÿP>|z|ÿÿÿÿÿ[95%ÿConf.ÿInterval]
-------------+----------------------------------------------------------------
Measurementÿÿ|
ÿÿy1ÿ<-ÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿFÿ|ÿÿÿ.9508349ÿÿÿ.0543566ÿÿÿÿ17.49ÿÿÿ0.000ÿÿÿÿÿ.8442978ÿÿÿÿ1.057372
ÿÿ-----------+----------------------------------------------------------------
ÿÿy2ÿ<-ÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿFÿ|ÿÿÿ.9134666ÿÿÿ.0528883ÿÿÿÿ17.27ÿÿÿ0.000ÿÿÿÿÿ.8098074ÿÿÿÿ1.017126
ÿÿ-----------+----------------------------------------------------------------
ÿÿy3ÿ<-ÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿFÿ|ÿÿÿ.9530369ÿÿÿ.0540701ÿÿÿÿ17.63ÿÿÿ0.000ÿÿÿÿÿ.8470615ÿÿÿÿ1.059012
ÿÿ-----------+----------------------------------------------------------------
ÿÿy4ÿ<-ÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿFÿ|ÿÿÿÿ.909055ÿÿÿ.0529553ÿÿÿÿ17.17ÿÿÿ0.000ÿÿÿÿÿ.8052646ÿÿÿÿ1.012845
ÿÿ-----------+----------------------------------------------------------------
ÿÿy5ÿ<-ÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿFÿ|ÿÿÿ2.798833ÿÿÿ.1213234ÿÿÿÿ23.07ÿÿÿ0.000ÿÿÿÿÿ2.561044ÿÿÿÿ3.036623
-------------+----------------------------------------------------------------
ÿÿÿÿvar(e.y1)|ÿÿÿ.4135064ÿÿÿ.0372984ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.3465002ÿÿÿÿ.4934703
ÿÿÿÿvar(e.y2)|ÿÿÿ.4024421ÿÿÿ.0360094ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.3377071ÿÿÿÿ.4795862
ÿÿÿÿvar(e.y3)|ÿÿÿÿ.400344ÿÿÿ.0366341ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.334613ÿÿÿÿÿ.478987
ÿÿÿÿvar(e.y4)|ÿÿÿ.4094857ÿÿÿ.0363706ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.3440605ÿÿÿÿ.4873519
ÿÿÿÿvar(e.y5)|ÿÿÿ.3820561ÿÿÿÿ.114871ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.2119339ÿÿÿÿ.6887378
ÿÿÿÿÿÿÿvar(F)|ÿÿÿÿÿÿÿÿÿÿ1ÿÿ(constrained)
------------------------------------------------------------------------------
LRÿtestÿofÿmodelÿvs.ÿsaturated:ÿchi2(5)ÿÿÿ=ÿÿÿÿÿÿ2.30,ÿProbÿ>ÿchi2ÿ=ÿ0.8061

.ÿ
.ÿscalarÿdefineÿLÿ=ÿ0

.ÿscalarÿdefineÿEÿ=ÿ0

.ÿforvaluesÿiÿ=ÿ1/5ÿ{
ÿÿ2.ÿÿÿÿÿÿÿÿÿscalarÿdefineÿLÿ=ÿLÿ+ÿ_b[y`i':F]
ÿÿ3.ÿÿÿÿÿÿÿÿÿscalarÿdefineÿEÿ=ÿEÿ+ÿ_b[var(e.y`i'):_cons]
ÿÿ4.ÿ}

.ÿdisplayÿinÿsmclÿasÿtextÿ"Rhoÿ=ÿ"ÿasÿresultÿ%06.4fÿL^2ÿ/ÿ(L^2ÿ+ÿE)
Rhoÿ=ÿ0.9550

.ÿ
.ÿ//ÿor
.ÿ
.ÿlocalÿLÿ_b[y1:F]

.ÿlocalÿEÿ_b[var(e.y1):_cons]

.ÿforvaluesÿiÿ=ÿ2/5ÿ{
ÿÿ2.ÿÿÿÿÿÿÿÿÿlocalÿLÿ`L'ÿ+ÿ_b[y`i':F]
ÿÿ3.ÿÿÿÿÿÿÿÿÿlocalÿEÿ`E'ÿ+ÿ_b[var(e.y`i'):_cons]
ÿÿ4.ÿ}

.ÿnlcomÿrho:ÿ(`L')^2ÿ/ÿ((`L')^2ÿ+ÿ`E'),ÿnoheader

------------------------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿÿÿÿÿ|ÿÿÿÿÿÿCoef.ÿÿÿStd.ÿErr.ÿÿÿÿÿÿzÿÿÿÿP>|z|ÿÿÿÿÿ[95%ÿConf.ÿInterval]
-------------+----------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿrhoÿ|ÿÿÿ.9549676ÿÿÿÿ.004421ÿÿÿ216.01ÿÿÿ0.000ÿÿÿÿÿ.9463025ÿÿÿÿ.9636326
------------------------------------------------------------------------------

.ÿ
.ÿexit

endÿofÿdo-file


.

So, for yours, assuming that you don't contemplate covariance between indicator variables, it would be something like

sem (x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 <- F), variance(F@1) nocnsreport nodescribe nolog
local L _b[x1:F]
local E _b[var(e.x1):_cons]
forvalues i = 2/10 {
    local L `L' + _b[x`i':F]
    local E `E' + _b[var(e.x`i'):_cons]
}
nlcom rho: (`L')^2 / ((`L')^2 + `E'), noheader

[Senor Massao]

Hi,

Thank you very much. I got this in stata now.
By the way, for some strange reason, I get a slightly different answer in MPlus. It's probably not the right forum to put out the Mplus code for this, but this is how it looks:

Analysis:
ESTIMATOR = ML;
BOOTSTRAP = 2000;

MODEL:

X1 (resv1);
X2( resv2);
X3 (resv3);
X4 (resv4);
X5 (resv5);
X6 (resv6);
X7 (resv7);
X8 (resv8);
X9 (resv9);
X10 (resv10);

f by X1;
f by X2(l2);
f by X3(l3);
f by X4(l4);
f by X5(l5);
f by X6(l6);
f by X7(l7);
f by X8(l8);
f by X9(l9);
f by X10(l10);


f@1;

MODEL CONSTRAINT:

NEW(omega);
omega =(1+l2+l3+l4+l5+l6+l7+l8+l9+l10)^2/
((1+l2+l3+l4+l5+l6+l7+l8+l9+l10)^2+
resv1+resv2+resv3+resv4+resv5+resv6+resv7+resv8+re sv9+resv10);

OUTPUT:
CINTERVAL(BCBOOTSTRAP);

[Joseph Coveney]

Free your first factor loading.

F BY X1* (L1);

and modify the constraint equation accordingly.

[Senor Massao]

Thanks :-)

[Tingting Tan]

Hi,

I am new to this forum as well as to using Stata for this type of analysis. In running your Stata codes using the Raycov example, I kept getting the error message saying "invalid syntax" for the last line, "
nlcom rho: (`L')^2 / ((`L')^2 + `E'), noheader I couldn't figure out why as the previous lines ran without any hiccups. I'd appreciate your help.