Formative and reflective indicators SEM

[Tamaryn Friderichs]

Hi,

I am trying to estimate a latent variable (human capital - HC) which has formative indicators eg education, age, gender, etc and a reflective indicator income. Which command would I look into to do this? I originally thought using the SEM builder but now I see that PLSSEM maybe the correct way to go. The theory says I should estimate HC using a linear combination of formative indicators that gives the best fit to the only reflective indicator (income). The other problem I have is that I have both categorical and quantitative indicators. I have converted the categorical indicators to dummy variables. Here the literature says to use MORALS (within the ALSOS methods) to quantify the categorical variables.

It also states that the solutions obtained "by means of the Factor Model are not unique and that the solutions obtained by the PLS Method are not logically consistent" so to overcome these the information embedded in the Path Analysis model should be used. This has now completely confused me as then it seems that PLSSEM should not be used.

Please can you point me in the correct direction of which commands I should be looking into. Or any help please.

Once I have the latent variable HC I am going to use it to look at descriptive statistics as well as to look at the distribution. So this is the reason I want to construct the HC latent variable.

Many thanks! Tamaryn

[Phil Bromiley]

Welcome to Statalist. You didn't get a quick answer. You'll increase your chances of a useful answer by following the FAQ on asking questions - provide Stata code in code delimiters, readable Stata output, and sample data using dataex. When you refer to "the literature", be more specific - let us know what paper (and the full citation).

It is a little unusual to have both formative and reflective indicators for the same latent variable, but I don't see why you can't just set this up as a standard sem where you have each of the formative indicators influencing the latent variable and the latent variable influencing the reflective indicator.

While PLS has some advocates, a number of scholars think it is a technique that has little value and should not be used.

[Tamaryn Friderichs]

Dear Phil, thank you that is helpful. The main authors on this are Vittadini and Lovaglio (2007) as well as the late Dagum in the paper Dagum et al (2007). I will try get the data into a sample format. I dont think that PLS is necessary but rather that human capital is estimated with formative indicators such as years of education etc and at the same time the reflective indicator household income. I found that for the latent variable household human capital (HK) when I predicted it using "predict HK, latent" I got some negative outcomes. This is confusing me slightly .

I did a simple example first to test run the data etc using just household heads years of education (hhheducyrs) and then the years of education of the household spouse (hhseducyrs_hhh) and household income (hhincome)

The code I used is:

sem (HK -> hhheducyrs, ) (HK -> hhseducyrs_hhh, ) (HK -> hhincome,), method(mlmv) standardized latent(HK ) nocapslatent

predict HK, latent

The diagram I used. Is the diagram correct for measuring HK using formative indicators of years of education and simultaneously the reflective indicator of household income.

If all of the above is correct then why would I be getting negative results for Human Capital

I will upload the sample data shortly

[Tamaryn Friderichs]

Data - hope this is correct format

clear
input float(hhheducyrs hhseducyrs_hhh hhincome)
16 8 20000
16 8 18900
16 10 28000
16 10 22760
16 10 7000
16 10 8405.216
16 10 166000
16 11 11500
16 11 31400
16 11 38395.42
16 11 41700
16 11 4000
16 11 69754.17
16 12 40838.37
16 12 58000
16 12 68000
16 12 24000
16 12 26425
16 12 21473.79
16 12 39500
16 12 48525.74
16 12 51000
16 12 19000
16 12 22609
16 12 70000
16 12 94000
16 12 62000
16 12 245000
16 12 15663.796
16 12 35000
16 12 26000
16 12 8600
16 12 57206.41
16 12 35000
16 12 27425.266
16 12 33000
16 12 77290.08
16 12 110814.72
16 12 42000
16 12 50000
16 12 6000
16 12 13800
16 12 14000
16 13 27000
16 13 40000
16 13 36000
16 13 37936.36
16 13 21477.12
16 13 78500
16 13 30200
16 13 79000
16 13 70000
16 13 33601.977
16 13 46580
16 13 156394.63
16 13 78926
16 13 61391.75
16 13 35951.42
16 13 42500
16 13 42869.43
16 13 35360
16 13 15540.656
16 13 70000
16 13 52000
16 13 111419
16 13 55000
16 13 21700
16 13 34600
16 13 175000
16 13 106500
16 13 11720
16 13 45000
16 13 26100
16 13 40311
16 13 48500
16 13 85500
16 13 85000
16 13 38300
16 13 24700
16 15 95972.05
16 15 32000
16 15 170000
16 15 25500
16 15 45000
16 15 49000
16 15 53000
16 15 81020
16 15 60000
16 15 63385.2
16 15 78500
16 15 63500
16 15 59000
16 15 27640
16 15 20019.176
16 15 70000
16 15 71162.09
16 16 60587.7
16 16 71600
16 16 120738.91
16 16 140000
end
[/CODE]

[Joseph Coveney]

. . .formative indicators eg education, age, gender, etc and a reflective indicator income. . . . theory says I should estimate . . . using a linear combination of formative indicators that gives the best fit to the only reflective indicator (income).

Wouldn't that latter imply just something like

regress income c.education c.age i.gender etc

I thought that the main purpose of SEM of latent factors with formative indicators was to hold the regression coefficients of the predictors equal. Did I get that wrong?

[Tamaryn Friderichs]

I was also wondering which will be the best gini command to run if I have negative values. when I run fastgini I get a result of 0.59 but for the others (inequal7, pshare, gini) I get 4.7e+09 which I am unsure how to interpret but I am thinking that it is not clear to have a negative measure for human capital so that might be my problem to start.

[Tamaryn Friderichs]

Wouldn't that latter imply just something like

regress income c.education c.age i.gender etc

I thought that the main purpose of SEM of latent factors with formative indicators was to hold the regression coefficients of the predictors equal. Did I get that wrong?

Thank you Joseph - if this is correct then that will be very helpful. Can anyone else possibly give some feedback on this please.

[Tamaryn Friderichs]

But in the case of regress income c.education c.age i.gender - how would I predict the latent variable human capital? The reason I thought SEM was because of the need for the latent construct.

Could the direction of the arrows in my SEM builder not be incorrect. The way I reasoned it is HK is dependent on education etc (hhheducyrs hhseducyrs_hhh) and then it causes household income (hhincome). I did try run it with the arrows in different directions but it resulted in numerous iterations and never concluded in a result.