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# Re: st: CR and AVE for factor analysis with 2 factors

 From Nick Cox <[email protected]> To "[email protected]" <[email protected]> Subject Re: st: CR and AVE for factor analysis with 2 factors Date Tue, 29 Oct 2013 09:28:29 +0000

```What's e(df_m) in your case?
Nick
[email protected]

On 29 October 2013 09:07, Florian Christian Esser
<[email protected]> wrote:
> Here we go (I included the uniqueness and the loadings as well).
> Communalities are on the bottom:
> _____________________________________________________________
>
>
> . matrix list e(Psi)
>
> e(Psi)[1,6]
>             zwmdiff_1  zwpdiff_1  zwpdiff_2   zwcost_1   zwcost_2   zwcost_3
> Uniqueness  .14721836  .16061008  .12541414  .01425274  .01366305  .02630422
>
> . matrix list e(L)
>
> e(L)[6,3]
>               Factor1     Factor2     Factor3
> zwmdiff_1   .81629684     .233233   .36337787
> zwpdiff_1   .82275816   .39938175  -.05434294
> zwpdiff_2    .8671496   .34761446   .04244559
>  zwcost_1  -.52875169   .83417333   .10160593
>  zwcost_2  -.51348298   .84223386   .11538764
>  zwcost_3  -.18959666  -.28021389    .9269461
>
> . matrix psi = e(Psi)'
>
> . matrix communalities = J(rowsof(psi),1,1)
>
> . matrix communalities = communalities - psi
>
> . matrix colnames communalities = communalities
>
> . matrix list communalities
>
> communalities[6,1]
>            communalit~s
> zwmdiff_1     .85278164
> zwpdiff_1     .83938992
> zwpdiff_2     .87458586
>  zwcost_1     .98574726
>  zwcost_2     .98633695
>  zwcost_3     .97369578
> _____________________________________________________
>
>> What is implied by your log is that
>>
>> replace sum_factors = sum_factors + sqrt(communalities[3,1])
>>
>> has the effect of replacing -sum_factors- with missing. So, please
>> show us that -communalities- matrix,
>> namely the result of your line
>>
>> matrix list communalities
>>
>> (I see on closer examination that the -communalities- matrix is not
>> the communalaties as first reported, but modified.)
>>
>> firmly a PCA person.
>> Nick
>> [email protected]
>>
>>
>> On 29 October 2013 07:14, Florian Christian Esser
>> <[email protected]> wrote:
>>> Unfortunately, all my communalities are positive.
>>> Does anyone have any ideas, what else could cause the issue?
>>>
>>> Is the general approach correct, to calculate CR and AVE for both
>>> factors
>>> at the same time, or would I have to do it individually. I.e. I do the
>>> factor analysis, identify, that the indicators load on two factors and
>>> then calculate CR and AVE for each factor individually?
>>>
>>>> Your missing value is presumably the result of taking the square root
>>>> of a negative number. Is at least one of your communalities reported
>>>> as negative?
>>>>
>>>> That aside you have segments like
>>>>
>>>> gen nvar = e(df_m)
>>>> gen sum_factors=0
>>>> local i=1
>>>> while `i' <= nvar {
>>>> replace sum_factors = sum_factors + sqrt(communalities[`i',1])
>>>> local i=`i'+1
>>>> }
>>>>
>>>> You can simplify this. First, to hold constants, use locals or
>>>> scalars, not variables. Second, use -forval- to loop here:
>>>>
>>>> local nvar = e(df_m)
>>>> local sum_factors = 0
>>>> forval i = 1/`nvar' {
>>>>      local sum_factors = `sum_factors'  + sqrt(communalities[`i',1]
>>>> }
>>>>
>>>> Third, use Mata instead. Here is a self-contained example:
>>>>
>>>> . matrix foo = (1,2,3,4)
>>>>
>>>> . mata : st_numscalar("sum_factors", sum(sqrt(st_matrix("foo"))))
>>>>
>>>> . scalar li
>>>> sum_factors =  6.1462644
>>>>
>>>> However, none of these tricks can get round what appears to be your
>>>> problem.
>>>>
>>>>
>>>> Nick
>>>> [email protected]
>>>>
>>>>
>>>> On 28 October 2013 14:11, Florian Christian Esser
>>>> <[email protected]> wrote:
>>>>> Hi everyone,
>>>>>
>>>>> I am trying to do factor analysis in order to measure two strategy
>>>>> constructs. I have 6 indicators that load on these two constructs. Now
>>>>> I
>>>>> want to calculate composite reliability (CR) and average variance
>>>>> extracted(AVE).
>>>>> I use the following code (here for CR):
>>>>> ___________________________________________________________________
>>>>> factor zwmdiff_1 zwpdiff_1 zwpdiff_2 zwcost_1 zwcost_2 zwcost_3, pcf
>>>>> matrix list e(Psi)
>>>>> matrix list e(L)
>>>>> matrix psi = e(Psi)'
>>>>> matrix communalities = J(rowsof(psi),1,1)
>>>>> matrix communalities = communalities - psi
>>>>> matrix colnames communalities = communalities
>>>>> matrix list communalities
>>>>> gen nvar = e(df_m)
>>>>> gen sum_factors=0
>>>>> local i=1
>>>>> while `i' <= nvar {
>>>>> replace sum_factors = sum_factors + sqrt(communalities[`i',1])
>>>>> local i=`i'+1
>>>>> }
>>>>> generate sum_psi=0
>>>>> local i=1
>>>>> while `i' <= nvar {
>>>>> replace sum_psi = sum_psi + psi[`i',1]
>>>>> local i=`i'+1
>>>>> }
>>>>> gen cr=(sum_factors*sum_factors)/((sum_factors*sum_factors)+sum_psi)
>>>>> drop nvar
>>>>> drop sum_factors
>>>>> drop sum_psi
>>>>> list cr in 1
>>>>> _________________________________________________________________
>>>>>
>>>>> The problem is that once the local macro starts running it tells me:
>>>>> _____________________________
>>>>> [...]
>>>>> (534 real changes made, 534 to missing)
>>>>> [...]
>>>>> ___________________________
>>>>>
>>>>> and accordingly there is an empty result for CR.
>>>>> If I add "factors(1)" in the command line above, I get a result, but I
>>>>> since I have two factors, I think it is not correct to do this.
>>>>>
>>>>> Does anyone know what to do here?
>>>>>
>>>>> Thanks a lot in advance.
>>>>>
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>
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```