SEM CFA with higher-order factor not converging

Zach Goldberg

Join Date: Jul 2017
Posts: 184

SEM CFA with higher-order factor not converging

09 Feb 2021, 12:07

Greetings,

I'm running Stata 15.1 on a Mac OS and am working with cross-sectional survey data. I'm trying to run a CFA of two factors (RR, DISC) with one higher-order factor (GF):

Code:

sem (RR-> revrr_favors revrr_tryharder rr_slavery rr_deserve) (DISC->  racineq_discrim disc_blacks nodisc_equalincomes) (GF->RR DISC) if white==1, stand method(adf)

However, after entering the syntax above, I am unable to get the model to converge (it endlessly iterates). I'm not sure what the issue is, so I would really appreciate some input on how to correct it.

Here is some sample data:

Code:

* Example generated by -dataex-. To install: ssc install dataex
clear
input byte(revrr_favors revrr_tryharder) long(rr_slavery rr_deserve)    byte    racineq_discrim    long(disc_blacks    nodisc_equalincomes)    byte    white
5 5 5 5   0 5 2 1
4 3 4 3  50 3 3 0
4 4 4 4  75 5 6 1
1 3 1 1   9 1 4 1
4 5 5 3  50 5 4 1
2 3 4 2  15 3 4 1
2 4 5 3  70 4 4 1
5 5 5 5 100 5 6 1
3 3 4 4  75 3 4 1
1 1 2 2  48 4 2 1
5 5 5 5  80 5 6 1
1 1 1 1  10 2 1 1
5 5 5 5  85 5 6 1
5 5 5 5 100 5 7 1
4 4 5 4  76 5 5 1
5 4 2 3  55 4 3 1
1 1 1 1   0 1 1 1
4 4 4 5  55 5 5 1
1 2 1 1   0 1 1 1
3 3 3 3  51 4 4 1
4 5 4 5  50 4 4 1
5 5 5 5  90 5 4 0
1 3 2 2  20 3 5 1
1 1 1 1   0 2 1 1
4 5 5 5  56 4 5 1
2 4 5 4  70 4 6 1
5 5 5 5 100 5 7 1
5 5 1 5 100 5 4 1
3 4 2 3  30 4 5 1
2 4 3 1  18 2 4 1
4 2 4 4  95 3 7 1
3 4 2 3   8 3 2 0
5 5 5 5  90 5 6 0
5 5 5 5 100 4 7 1
2 2 3 2  63 2 2 1
3 3 3 2  65 3 6 1
5 5 1 4  80 5 7 1
4 4 4 4  80 4 5 1
5 5 5 5  90 4 7 1
1 1 1 1  25 1 4 1
1 1 1 1  25 1 1 1
4 5 5 5  89 4 7 1
5 5 4 5 100 5 6 1
2 3 4 5  57 5 7 1
3 3 1 1   0 3 2 1
4 4 4 4  79 4 5 1
5 4 4 5  71 4 3 1
2 5 2 2   5 2 2 1
5 5 5 5 100 4 7 1
1 1 1 1   2 2 1 1
3 4 3 3  21 3 3 1
5 5 5 5  60 5 5 1
4 4 3 3  60 3 3 1
4 5 4 5  80 4 4 1
4 4 5 4  71 3 5 1
2 3 4 3  50 3 5 1
2 2 3 3  50 3 5 1
3 4 5 2   0 1 4 1
3 4 4 3  50 3 4 1
1 2 4 2  40 3 3 1
4 4 4 4  64 3 3 1
1 1 1 1  10 2 2 1
2 4 5 5  80 5 7 1
2 5 4 3  51 4 3 1
5 5 5 5  90 5 7 1
2 3 4 1   5 3 3 1
5 5 5 5  87 5 6 1
4 5 1 5  93 5 5 1
2 4 4 3  50 3 4 1
5 5 5 5  90 5 7 1
5 5 5 5  85 5 6 1
1 1 1 1  54 3 6 1
1 1 1 1   8 3 2 1
3 4 4 4  50 4 4 1
4 4 4 3  51 3 1 1
2 2 4 2  25 3 4 0
4 5 5 5  90 4 7 1
3 4 4 4  86 4 4 1
5 4 5 5  82 5 5 1
2 3 3 3  20 3 3 1
3 4 4 4  51 4 7 1
5 4 5 5  80 4 4 1
1 3 1 2  10 2 4 1
3 5 5 5 100 5 7 1
4 3 4 4  60 4 6 1
4 4 5 4  60 3 5 1
5 5 5 3 100 5 7 1
4 4 4 3  60 4 4 1
5 5 5 3  95 5 5 1
2 2 4 5  50 5 5 1
5 5 5 5 100 5 6 1
3 5 4 5  80 5 2 0
5 5 5 5  81 5 5 1
5 5 5 5 100 5 6 1
1 1 1 1  10 2 3 1
3 3 4 3  61 3 5 1
5 5 5 5  95 3 6 1
2 5 4 4  70 4 5 0
2 3 3 3  31 4 5 1
5 5 5 5 100 5 6 1
end
label values revrr_favors revrr_favors
label def revrr_favors 1 "Strongly agree", modify
label def revrr_favors 2 "Somewhat agree", modify
label def revrr_favors 3 "Neither agree nor disagree", modify
label def revrr_favors 4 "Somewhat disagree", modify
label def revrr_favors 5 "Strongly disagree", modify
label values revrr_tryharder revrr_tryharder
label def revrr_tryharder 1 "Strongly agree", modify
label def revrr_tryharder 2 "Somewhat agree", modify
label def revrr_tryharder 3 "Neither agree nor disagree", modify
label def revrr_tryharder 4 "Somewhat disagree", modify
label def revrr_tryharder 5 "Strongly disagree", modify
label values rr_slavery rr_slavery
label def rr_slavery 1 "Strongly disagree", modify
label def rr_slavery 2 "Somewhat disagree", modify
label def rr_slavery 3 "Neither agree nor disagree", modify
label def rr_slavery 4 "Somewhat agree", modify
label def rr_slavery 5 "Strongly agree", modify
label values rr_deserve rr_deserve
label def rr_deserve 1 "Strongly disagree", modify
label def rr_deserve 2 "Somewhat disagree", modify
label def rr_deserve 3 "Neither agree nor disagree", modify
label def rr_deserve 4 "Somewhat agree", modify
label def rr_deserve 5 "Strongly agree", modify
label values disc_blacks disc_blacks
label def disc_blacks 1 "None at all", modify
label def disc_blacks 2 "Only a little", modify
label def disc_blacks 3 "Some", modify
label def disc_blacks 4 "A lot", modify
label def disc_blacks 5 "A great deal", modify
label values nodisc_equalincomes nodisc_equalincomes
label def nodisc_equalincomes 1 "Strongly disagree", modify
label def nodisc_equalincomes 2 "Disagree", modify
label def nodisc_equalincomes 3 "Somewhat disagree", modify
label def nodisc_equalincomes 4 "Neither agree nor disagree", modify
label def nodisc_equalincomes 5 "Somewhat agree", modify
label def nodisc_equalincomes 6 "Agree", modify
label def nodisc_equalincomes 7 "Strongly agree", modify

Thanks in advance for your help!

Tags: None

Weiwen Ng

Join Date: Jun 2015

Posts: 1241
#2

09 Feb 2021, 12:57

You need at least three first-order factors to identify a second-order model. Or, as the link says, you can constrain the loadings of both first-order factors on the second to be 1, but I'm not sure of a theoretical justification for that. Basically, with your current data and your current theoretical framework, there is nothing you can do to estimate a second-order factor model. I know that identification is pretty complex, but the outline of the issue is that you need at least one more piece of information to identify the higher-order factor, or else there is no unique solution to all the parameters. Remember those algebra problems where they give you two equations with two unknowns, and you have to solve for each unknown? I'm probably oversimplifying, but identification in SEM is as if you were given one equation with two unknowns - you can't find a unique solution for both unknowns without one more equation.

Be aware that it can be very hard to answer a question without sample data. You can use the dataex command for this. Type help dataex at the command line.

When presenting code or results, please use the code delimiters format them. Use the # button on the formatting toolbar, between the " (double quote) and <> buttons.
Comment
Zach Goldberg

Join Date: Jul 2017

Posts: 184
#3

09 Feb 2021, 13:35

Hey Weiwen,

Thanks for the reply. Out of curiosity, I tried splitting one of the first-order factors into two. But I still can't get it to converge:

Code:

sem (RR-> revrr_favors revrr_tryharder) (DISC2->rr_slavery rr_deserve) (DISC1-> racineq_discrim disc_blacks nodisc_equalincomes) (GF->RR DISC1 DISC2) if white==1, method(adf)
Comment

Zach Goldberg

Join Date: Jul 2017
Posts: 184

09 Feb 2021, 14:16

In fact, I can't even get it to converge if keep the original equation but add another factor:

Code:

sem (RR-> revrr_favors revrr_tryharder rr_slavery rr_deserve) (DISC->  racineq_discrim disc_blacks nodisc_equalincomes) (WPA-> wpa_advantages-wpa_easier) (GF->RR DISC WPA) if white==1, stand method(adf)

Some more sample data with the new variables:

Code:

* Example generated by -dataex-. To install: ssc install dataex
clear
input byte(revrr_favors revrr_tryharder) long(rr_slavery rr_deserve)    byte    racineq_discrim    long(disc_blacks    nodisc_equalincomes    wpa_advantages    wpa_opensdoors    wpa_easier)    byte    white
5 5 5 5   0 5 2 6 6 6 1
4 3 4 3  50 3 3 5 4 4 0
4 4 4 4  75 5 6 6 6 6 1
1 3 1 1   9 1 4 1 1 1 1
4 5 5 3  50 5 4 6 5 4 1
2 3 4 2  15 3 4 6 5 6 1
2 4 5 3  70 4 4 6 6 6 1
5 5 5 5 100 5 6 7 7 7 1
3 3 4 4  75 3 4 5 5 5 1
1 1 2 2  48 4 2 4 2 2 1
5 5 5 5  80 5 6 7 7 7 1
1 1 1 1  10 2 1 2 1 1 1
5 5 5 5  85 5 6 7 7 7 1
5 5 5 5 100 5 7 7 7 7 1
4 4 5 4  76 5 5 7 6 6 1
5 4 2 3  55 4 3 3 4 2 1
1 1 1 1   0 1 1 1 1 1 1
4 4 4 5  55 5 5 6 7 6 1
1 2 1 1   0 1 1 1 1 1 1
3 3 3 3  51 4 4 3 4 4 1
4 5 4 5  50 4 4 6 4 6 1
5 5 5 5  90 5 4 7 7 7 0
1 3 2 2  20 3 5 4 4 4 1
1 1 1 1   0 2 1 1 1 1 1
4 5 5 5  56 4 5 6 6 6 1
2 4 5 4  70 4 6 7 7 7 1
5 5 5 5 100 5 7 7 7 7 1
5 5 1 5 100 5 4 7 7 7 1
3 4 2 3  30 4 5 3 3 3 1
2 4 3 1  18 2 4 4 2 2 1
4 2 4 4  95 3 7 5 5 6 1
3 4 2 3   8 3 2 4 3 3 0
5 5 5 5  90 5 6 7 7 7 0
5 5 5 5 100 4 7 7 7 7 1
2 2 3 2  63 2 2 2 2 2 1
3 3 3 2  65 3 6 4 5 3 1
5 5 1 4  80 5 7 7 7 7 1
4 4 4 4  80 4 5 7 7 7 1
5 5 5 5  90 4 7 7 7 7 1
1 1 1 1  25 1 4 2 2 1 1
1 1 1 1  25 1 1 1 1 1 1
4 5 5 5  89 4 7 6 6 6 1
5 5 4 5 100 5 6 7 6 7 1
2 3 4 5  57 5 7 5 5 6 1
3 3 1 1   0 3 2 4 4 4 1
4 4 4 4  79 4 5 6 6 6 1
5 4 4 5  71 4 3 7 7 7 1
2 5 2 2   5 2 2 2 1 2 1
5 5 5 5 100 4 7 6 6 6 1
1 1 1 1   2 2 1 1 1 1 1
3 4 3 3  21 3 3 3 3 3 1
5 5 5 5  60 5 5 6 6 6 1
4 4 3 3  60 3 3 5 5 5 1
4 5 4 5  80 4 4 6 5 6 1
4 4 5 4  71 3 5 5 5 6 1
2 3 4 3  50 3 5 6 6 4 1
2 2 3 3  50 3 5 5 5 5 1
3 4 5 2   0 1 4 1 4 1 1
3 4 4 3  50 3 4 4 4 3 1
1 2 4 2  40 3 3 2 2 2 1
4 4 4 4  64 3 3 5 5 5 1
1 1 1 1  10 2 2 2 4 4 1
2 4 5 5  80 5 7 1 1 4 1
2 5 4 3  51 4 3 7 6 6 1
5 5 5 5  90 5 7 7 7 7 1
2 3 4 1   5 3 3 2 2 2 1
5 5 5 5  87 5 6 7 7 7 1
4 5 1 5  93 5 5 7 7 7 1
2 4 4 3  50 3 4 5 5 5 1
5 5 5 5  90 5 7 7 7 7 1
5 5 5 5  85 5 6 7 7 7 1
1 1 1 1  54 3 6 2 3 2 1
1 1 1 1   8 3 2 3 4 2 1
3 4 4 4  50 4 4 5 4 5 1
4 4 4 3  51 3 1 6 6 2 1
2 2 4 2  25 3 4 2 1 1 0
4 5 5 5  90 4 7 7 7 6 1
3 4 4 4  86 4 4 6 5 6 1
5 4 5 5  82 5 5 7 7 7 1
2 3 3 3  20 3 3 5 2 5 1
3 4 4 4  51 4 7 6 6 5 1
5 4 5 5  80 4 4 6 6 6 1
1 3 1 2  10 2 4 2 1 1 1
3 5 5 5 100 5 7 6 6 6 1
4 3 4 4  60 4 6 6 6 7 1
4 4 5 4  60 3 5 6 6 6 1
5 5 5 3 100 5 7 6 7 7 1
4 4 4 3  60 4 4 5 4 6 1
5 5 5 3  95 5 5 7 7 7 1
2 2 4 5  50 5 5 7 7 6 1
5 5 5 5 100 5 6 7 7 7 1
3 5 4 5  80 5 2 4 4 5 0
5 5 5 5  81 5 5 6 6 6 1
5 5 5 5 100 5 6 7 7 7 1
1 1 1 1  10 2 3 1 1 1 1
3 3 4 3  61 3 5 6 5 5 1
5 5 5 5  95 3 6 7 3 7 1
2 5 4 4  70 4 5 6 5 5 0
2 3 3 3  31 4 5 5 4 4 1
5 5 5 5 100 5 6 7 7 7 1
end
label values revrr_favors revrr_favors
label def revrr_favors 1 "Strongly agree", modify
label def revrr_favors 2 "Somewhat agree", modify
label def revrr_favors 3 "Neither agree nor disagree", modify
label def revrr_favors 4 "Somewhat disagree", modify
label def revrr_favors 5 "Strongly disagree", modify
label values revrr_tryharder revrr_tryharder
label def revrr_tryharder 1 "Strongly agree", modify
label def revrr_tryharder 2 "Somewhat agree", modify
label def revrr_tryharder 3 "Neither agree nor disagree", modify
label def revrr_tryharder 4 "Somewhat disagree", modify
label def revrr_tryharder 5 "Strongly disagree", modify
label values rr_slavery rr_slavery
label def rr_slavery 1 "Strongly disagree", modify
label def rr_slavery 2 "Somewhat disagree", modify
label def rr_slavery 3 "Neither agree nor disagree", modify
label def rr_slavery 4 "Somewhat agree", modify
label def rr_slavery 5 "Strongly agree", modify
label values rr_deserve rr_deserve
label def rr_deserve 1 "Strongly disagree", modify
label def rr_deserve 2 "Somewhat disagree", modify
label def rr_deserve 3 "Neither agree nor disagree", modify
label def rr_deserve 4 "Somewhat agree", modify
label def rr_deserve 5 "Strongly agree", modify
label values disc_blacks disc_blacks
label def disc_blacks 1 "None at all", modify
label def disc_blacks 2 "Only a little", modify
label def disc_blacks 3 "Some", modify
label def disc_blacks 4 "A lot", modify
label def disc_blacks 5 "A great deal", modify
label values nodisc_equalincomes nodisc_equalincomes
label def nodisc_equalincomes 1 "Strongly disagree", modify
label def nodisc_equalincomes 2 "Disagree", modify
label def nodisc_equalincomes 3 "Somewhat disagree", modify
label def nodisc_equalincomes 4 "Neither agree nor disagree", modify
label def nodisc_equalincomes 5 "Somewhat agree", modify
label def nodisc_equalincomes 6 "Agree", modify
label def nodisc_equalincomes 7 "Strongly agree", modify
label values wpa_advantages wpa_advantages
label def wpa_advantages 1 "Strongly disagree", modify
label def wpa_advantages 2 "Disagree", modify
label def wpa_advantages 3 "Somewhat disagree", modify
label def wpa_advantages 4 "Neither agree nor disagree", modify
label def wpa_advantages 5 "Somewhat agree", modify
label def wpa_advantages 6 "Agree", modify
label def wpa_advantages 7 "Strongly agree", modify
label values wpa_opensdoors wpa_opensdoors
label def wpa_opensdoors 1 "Strongly disagree", modify
label def wpa_opensdoors 2 "Disagree", modify
label def wpa_opensdoors 3 "Somewhat disagree", modify
label def wpa_opensdoors 4 "Neither agree nor disagree", modify
label def wpa_opensdoors 5 "Somewhat agree", modify
label def wpa_opensdoors 6 "Agree", modify
label def wpa_opensdoors 7 "Strongly agree", modify
label values wpa_easier wpa_easier
label def wpa_easier 1 "Strongly disagree", modify
label def wpa_easier 2 "Disagree", modify
label def wpa_easier 3 "Somewhat disagree", modify
label def wpa_easier 4 "Neither agree nor disagree", modify
label def wpa_easier 5 "Somewhat agree", modify
label def wpa_easier 6 "Agree", modify
label def wpa_easier 7 "Strongly agree", modify

Comment

Joseph Coveney

Join Date: Apr 2014

Posts: 4375
#5

09 Feb 2021, 19:38

Originally posted by Zach Goldberg View Post

In fact, I can't even get it to converge if keep the original equation but add another factor:

Maybe it's because your data support only a single factor.

.ÿ
.ÿversionÿ16.1

.ÿ
.ÿclearÿ*

.ÿ
.ÿquietlyÿinputÿbyte(revrr_favorsÿrevrr_tryharder)ÿlong(rr_slaveryÿrr_deserve)ÿ///
>ÿÿÿÿÿÿÿÿÿbyteÿracineq_discrimÿlong(disc_blacksÿnodisc_equalincomesÿwpa_advantagesÿ///
>ÿÿÿÿÿÿÿÿÿwpa_opensdoorsÿwpa_easier)ÿbyteÿwhite

.ÿ
.ÿquietlyÿcompress

.ÿ
.ÿfactorÿrevrr_favors-wpa_easier
(obs=100)

Factorÿanalysis/correlationÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿNumberÿofÿobsÿÿÿÿ=ÿÿÿÿÿÿÿÿ100
ÿÿÿÿMethod:ÿprincipalÿfactorsÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿRetainedÿfactorsÿ=ÿÿÿÿÿÿÿÿÿÿ5
ÿÿÿÿRotation:ÿ(unrotated)ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿNumberÿofÿparamsÿ=ÿÿÿÿÿÿÿÿÿ40

ÿÿÿÿ--------------------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿFactorÿÿ|ÿÿÿEigenvalueÿÿÿDifferenceÿÿÿÿÿÿÿÿProportionÿÿÿCumulative
ÿÿÿÿ-------------+------------------------------------------------------------
ÿÿÿÿÿÿÿÿFactor1ÿÿ|ÿÿÿÿÿÿ7.35078ÿÿÿÿÿÿ7.08557ÿÿÿÿÿÿÿÿÿÿÿÿ0.9582ÿÿÿÿÿÿÿ0.9582
ÿÿÿÿÿÿÿÿFactor2ÿÿ|ÿÿÿÿÿÿ0.26522ÿÿÿÿÿÿ0.02162ÿÿÿÿÿÿÿÿÿÿÿÿ0.0346ÿÿÿÿÿÿÿ0.9928
ÿÿÿÿÿÿÿÿFactor3ÿÿ|ÿÿÿÿÿÿ0.24360ÿÿÿÿÿÿ0.18461ÿÿÿÿÿÿÿÿÿÿÿÿ0.0318ÿÿÿÿÿÿÿ1.0245
ÿÿÿÿÿÿÿÿFactor4ÿÿ|ÿÿÿÿÿÿ0.05899ÿÿÿÿÿÿ0.01710ÿÿÿÿÿÿÿÿÿÿÿÿ0.0077ÿÿÿÿÿÿÿ1.0322
ÿÿÿÿÿÿÿÿFactor5ÿÿ|ÿÿÿÿÿÿ0.04189ÿÿÿÿÿÿ0.04939ÿÿÿÿÿÿÿÿÿÿÿÿ0.0055ÿÿÿÿÿÿÿ1.0377
ÿÿÿÿÿÿÿÿFactor6ÿÿ|ÿÿÿÿÿ-0.00750ÿÿÿÿÿÿ0.02847ÿÿÿÿÿÿÿÿÿÿÿ-0.0010ÿÿÿÿÿÿÿ1.0367
ÿÿÿÿÿÿÿÿFactor7ÿÿ|ÿÿÿÿÿ-0.03598ÿÿÿÿÿÿ0.00217ÿÿÿÿÿÿÿÿÿÿÿ-0.0047ÿÿÿÿÿÿÿ1.0320
ÿÿÿÿÿÿÿÿFactor8ÿÿ|ÿÿÿÿÿ-0.03815ÿÿÿÿÿÿ0.04899ÿÿÿÿÿÿÿÿÿÿÿ-0.0050ÿÿÿÿÿÿÿ1.0270
ÿÿÿÿÿÿÿÿFactor9ÿÿ|ÿÿÿÿÿ-0.08714ÿÿÿÿÿÿ0.03297ÿÿÿÿÿÿÿÿÿÿÿ-0.0114ÿÿÿÿÿÿÿ1.0157
ÿÿÿÿÿÿÿFactor10ÿÿ|ÿÿÿÿÿ-0.12011ÿÿÿÿÿÿÿÿÿÿÿÿ.ÿÿÿÿÿÿÿÿÿÿÿ-0.0157ÿÿÿÿÿÿÿ1.0000
ÿÿÿÿ--------------------------------------------------------------------------
ÿÿÿÿLRÿtest:ÿindependentÿvs.ÿsaturated:ÿÿchi2(45)ÿ=ÿ1131.13ÿProb>chi2ÿ=ÿ0.0000

Factorÿloadingsÿ(patternÿmatrix)ÿandÿuniqueÿvariances

ÿÿÿÿ-------------------------------------------------------------------------------
ÿÿÿÿÿÿÿÿVariableÿ|ÿÿFactor1ÿÿÿFactor2ÿÿÿFactor3ÿÿÿFactor4ÿÿÿFactor5ÿ|ÿÿÿUniquenessÿ
ÿÿÿÿ-------------+--------------------------------------------------+--------------
ÿÿÿÿrevrr_favorsÿ|ÿÿÿ0.8568ÿÿÿÿ0.2147ÿÿÿ-0.1043ÿÿÿÿ0.0602ÿÿÿ-0.1108ÿ|ÿÿÿÿÿÿ0.1930ÿÿ
ÿÿÿÿrevrr_tryh~rÿ|ÿÿÿ0.8159ÿÿÿÿ0.2927ÿÿÿ-0.0582ÿÿÿÿ0.0332ÿÿÿÿ0.0325ÿ|ÿÿÿÿÿÿ0.2431ÿÿ
ÿÿÿÿÿÿrr_slaveryÿ|ÿÿÿ0.7574ÿÿÿÿ0.1200ÿÿÿÿ0.0945ÿÿÿÿ0.0732ÿÿÿÿ0.1172ÿ|ÿÿÿÿÿÿ0.3840ÿÿ
ÿÿÿÿÿÿrr_deserveÿ|ÿÿÿ0.9182ÿÿÿÿ0.1165ÿÿÿÿ0.0711ÿÿÿ-0.1177ÿÿÿÿ0.0214ÿ|ÿÿÿÿÿÿ0.1239ÿÿ
ÿÿÿÿracineq_di~mÿ|ÿÿÿ0.8646ÿÿÿ-0.0704ÿÿÿÿ0.2091ÿÿÿÿ0.0245ÿÿÿ-0.0950ÿ|ÿÿÿÿÿÿ0.1942ÿÿ
ÿÿÿÿÿdisc_blacksÿ|ÿÿÿ0.8505ÿÿÿ-0.0106ÿÿÿÿ0.0124ÿÿÿ-0.1490ÿÿÿ-0.0232ÿ|ÿÿÿÿÿÿ0.2537ÿÿ
ÿÿÿÿnodisc_equ~sÿ|ÿÿÿ0.7157ÿÿÿ-0.1320ÿÿÿÿ0.3067ÿÿÿÿ0.0618ÿÿÿÿ0.0194ÿ|ÿÿÿÿÿÿ0.3722ÿÿ
ÿÿÿÿwpa_advant~sÿ|ÿÿÿ0.9232ÿÿÿ-0.1563ÿÿÿ-0.2134ÿÿÿÿ0.0188ÿÿÿÿ0.0513ÿ|ÿÿÿÿÿÿ0.0748ÿÿ
ÿÿÿÿwpa_opensd~sÿ|ÿÿÿ0.9024ÿÿÿ-0.1914ÿÿÿ-0.1646ÿÿÿÿ0.0737ÿÿÿ-0.0301ÿ|ÿÿÿÿÿÿ0.1155ÿÿ
ÿÿÿÿÿÿwpa_easierÿ|ÿÿÿ0.9405ÿÿÿ-0.1481ÿÿÿ-0.0693ÿÿÿ-0.0516ÿÿÿÿ0.0297ÿ|ÿÿÿÿÿÿ0.0851ÿÿ
ÿÿÿÿ-------------------------------------------------------------------------------

.ÿ
.ÿquietlyÿpolychoricÿrevrr_favors-wpa_easier

.ÿtempnameÿRho

.ÿmatrixÿdefineÿ`Rho'ÿ=ÿr(R)

.ÿlocalÿNÿ`r(N)'

.ÿfactormatÿ`Rho',ÿn(`N')
(obs=100)

Factorÿanalysis/correlationÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿNumberÿofÿobsÿÿÿÿ=ÿÿÿÿÿÿÿÿ100
ÿÿÿÿMethod:ÿprincipalÿfactorsÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿRetainedÿfactorsÿ=ÿÿÿÿÿÿÿÿÿÿ6
ÿÿÿÿRotation:ÿ(unrotated)ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿNumberÿofÿparamsÿ=ÿÿÿÿÿÿÿÿÿ45

ÿÿÿÿ--------------------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿFactorÿÿ|ÿÿÿEigenvalueÿÿÿDifferenceÿÿÿÿÿÿÿÿProportionÿÿÿCumulative
ÿÿÿÿ-------------+------------------------------------------------------------
ÿÿÿÿÿÿÿÿFactor1ÿÿ|ÿÿÿÿÿÿ7.88681ÿÿÿÿÿÿ7.60124ÿÿÿÿÿÿÿÿÿÿÿÿ0.9451ÿÿÿÿÿÿÿ0.9451
ÿÿÿÿÿÿÿÿFactor2ÿÿ|ÿÿÿÿÿÿ0.28556ÿÿÿÿÿÿ0.02939ÿÿÿÿÿÿÿÿÿÿÿÿ0.0342ÿÿÿÿÿÿÿ0.9794
ÿÿÿÿÿÿÿÿFactor3ÿÿ|ÿÿÿÿÿÿ0.25617ÿÿÿÿÿÿ0.17985ÿÿÿÿÿÿÿÿÿÿÿÿ0.0307ÿÿÿÿÿÿÿ1.0101
ÿÿÿÿÿÿÿÿFactor4ÿÿ|ÿÿÿÿÿÿ0.07632ÿÿÿÿÿÿ0.04343ÿÿÿÿÿÿÿÿÿÿÿÿ0.0091ÿÿÿÿÿÿÿ1.0192
ÿÿÿÿÿÿÿÿFactor5ÿÿ|ÿÿÿÿÿÿ0.03288ÿÿÿÿÿÿ0.02623ÿÿÿÿÿÿÿÿÿÿÿÿ0.0039ÿÿÿÿÿÿÿ1.0232
ÿÿÿÿÿÿÿÿFactor6ÿÿ|ÿÿÿÿÿÿ0.00665ÿÿÿÿÿÿ0.02343ÿÿÿÿÿÿÿÿÿÿÿÿ0.0008ÿÿÿÿÿÿÿ1.0240
ÿÿÿÿÿÿÿÿFactor7ÿÿ|ÿÿÿÿÿ-0.01678ÿÿÿÿÿÿ0.01042ÿÿÿÿÿÿÿÿÿÿÿ-0.0020ÿÿÿÿÿÿÿ1.0219
ÿÿÿÿÿÿÿÿFactor8ÿÿ|ÿÿÿÿÿ-0.02719ÿÿÿÿÿÿ0.03617ÿÿÿÿÿÿÿÿÿÿÿ-0.0033ÿÿÿÿÿÿÿ1.0187
ÿÿÿÿÿÿÿÿFactor9ÿÿ|ÿÿÿÿÿ-0.06337ÿÿÿÿÿÿ0.02916ÿÿÿÿÿÿÿÿÿÿÿ-0.0076ÿÿÿÿÿÿÿ1.0111
ÿÿÿÿÿÿÿFactor10ÿÿ|ÿÿÿÿÿ-0.09253ÿÿÿÿÿÿÿÿÿÿÿÿ.ÿÿÿÿÿÿÿÿÿÿÿ-0.0111ÿÿÿÿÿÿÿ1.0000
ÿÿÿÿ--------------------------------------------------------------------------
ÿÿÿÿLRÿtest:ÿindependentÿvs.ÿsaturated:ÿÿchi2(45)ÿ=ÿ1412.41ÿProb>chi2ÿ=ÿ0.0000

Factorÿloadingsÿ(patternÿmatrix)ÿandÿuniqueÿvariances

ÿÿÿÿ-----------------------------------------------------------------------------------------
ÿÿÿÿÿÿÿÿVariableÿ|ÿÿFactor1ÿÿÿFactor2ÿÿÿFactor3ÿÿÿFactor4ÿÿÿFactor5ÿÿÿFactor6ÿ|ÿÿÿUniquenessÿ
ÿÿÿÿ-------------+------------------------------------------------------------+--------------
ÿÿÿÿrevrr_favorsÿ|ÿÿÿ0.9067ÿÿÿÿ0.2175ÿÿÿ-0.1074ÿÿÿÿ0.0560ÿÿÿ-0.0904ÿÿÿÿ0.0266ÿ|ÿÿÿÿÿÿ0.1070ÿÿ
ÿÿÿÿrevrr_tryh~rÿ|ÿÿÿ0.8658ÿÿÿÿ0.3018ÿÿÿ-0.0295ÿÿÿÿ0.0346ÿÿÿÿ0.0077ÿÿÿ-0.0191ÿ|ÿÿÿÿÿÿ0.1568ÿÿ
ÿÿÿÿÿÿrr_slaveryÿ|ÿÿÿ0.8276ÿÿÿÿ0.1432ÿÿÿÿ0.1295ÿÿÿÿ0.0952ÿÿÿÿ0.0870ÿÿÿ-0.0042ÿ|ÿÿÿÿÿÿ0.2612ÿÿ
ÿÿÿÿÿÿrr_deserveÿ|ÿÿÿ0.9459ÿÿÿÿ0.1040ÿÿÿÿ0.0781ÿÿÿ-0.1208ÿÿÿÿ0.0272ÿÿÿ-0.0015ÿ|ÿÿÿÿÿÿ0.0730ÿÿ
ÿÿÿÿracineq_di~mÿ|ÿÿÿ0.8485ÿÿÿ-0.1057ÿÿÿÿ0.1780ÿÿÿ-0.0052ÿÿÿ-0.1011ÿÿÿÿ0.0023ÿ|ÿÿÿÿÿÿ0.2270ÿÿ
ÿÿÿÿÿdisc_blacksÿ|ÿÿÿ0.8911ÿÿÿ-0.0148ÿÿÿ-0.0149ÿÿÿ-0.1909ÿÿÿÿ0.0357ÿÿÿÿ0.0214ÿ|ÿÿÿÿÿÿ0.1673ÿÿ
ÿÿÿÿnodisc_equ~sÿ|ÿÿÿ0.7430ÿÿÿ-0.1587ÿÿÿÿ0.3276ÿÿÿÿ0.0612ÿÿÿÿ0.0140ÿÿÿ-0.0021ÿ|ÿÿÿÿÿÿ0.3114ÿÿ
ÿÿÿÿwpa_advant~sÿ|ÿÿÿ0.9415ÿÿÿ-0.1523ÿÿÿ-0.2212ÿÿÿÿ0.0307ÿÿÿÿ0.0294ÿÿÿ-0.0385ÿ|ÿÿÿÿÿÿ0.0382ÿÿ
ÿÿÿÿwpa_opensd~sÿ|ÿÿÿ0.9258ÿÿÿ-0.1915ÿÿÿ-0.1583ÿÿÿÿ0.0818ÿÿÿÿ0.0408ÿÿÿÿ0.0499ÿ|ÿÿÿÿÿÿ0.0704ÿÿ
ÿÿÿÿÿÿwpa_easierÿ|ÿÿÿ0.9622ÿÿÿ-0.1393ÿÿÿ-0.0876ÿÿÿ-0.0216ÿÿÿ-0.0460ÿÿÿ-0.0334ÿ|ÿÿÿÿÿÿ0.0433ÿÿ
ÿÿÿÿ-----------------------------------------------------------------------------------------

.ÿ
.ÿexit

endÿofÿdo-file

.

Code:

search polychoric

to download and install that user-written command.
Comment
Zach Goldberg

Join Date: Jul 2017

Posts: 184
#6

09 Feb 2021, 23:16

That doesn't make sense to me. You should still be able to estimate such a model even if it poorly fits the data (relative to a single factor model).
Comment
Joseph Coveney

Join Date: Apr 2014

Posts: 4375
#7

10 Feb 2021, 04:42

Originally posted by Zach Goldberg View Post

That doesn't make sense to me. You should still be able to estimate such a model even if it poorly fits the data (relative to a single factor model).

In my experience, failure to converge is a cardinal symptom of a model that is so badly misspecified that little short of simplification can salvage it.

You've got basically a single dimension with an interitem correlation coefficient of 0.73 (see output from -alpha-below). Look what happens when I try to fit your model to a dataset that mimics those characteristics.

.ÿ
.ÿversionÿ16.1

.ÿ
.ÿclearÿ*

.ÿ
.ÿsetÿseedÿ`=strreverse("1593709")'

.ÿ
.ÿquietlyÿinputÿbyte(revrr_favorsÿrevrr_tryharder)ÿlong(rr_slaveryÿrr_deserve)ÿ///
>ÿÿÿÿÿÿÿÿÿbyteÿracineq_discrimÿlong(disc_blacksÿnodisc_equalincomesÿwpa_advantagesÿ///
>ÿÿÿÿÿÿÿÿÿwpa_opensdoorsÿwpa_easier)ÿbyteÿwhite

.ÿ
.ÿalphaÿrevrr_favors-wpa_easier,ÿstd

Testÿscaleÿ=ÿmean(standardizedÿitems)

Averageÿinteritemÿcorrelation:ÿÿÿÿÿÿ0.7262
Numberÿofÿitemsÿinÿtheÿscale:ÿÿÿÿÿÿÿÿÿÿÿ10
Scaleÿreliabilityÿcoefficient:ÿÿÿÿÿÿ0.9637

.ÿ
.ÿtempnameÿCorr

.ÿmatrixÿdefineÿ`Corr'ÿ=ÿJ(10,ÿ10,ÿr(rho))ÿ+ÿI(10)ÿ*ÿ(1ÿ-ÿr(rho))

.ÿforvaluesÿiÿ=ÿ1/10ÿ{
ÿÿ2.ÿÿÿÿÿÿÿÿÿlocalÿvarlistÿ`varlist'ÿv`i'
ÿÿ3.ÿ}

.ÿquietlyÿdrawnormÿ`varlist',ÿdoubleÿcorr(`Corr')ÿn(100)

.ÿ
.ÿsemÿ(v1-v4ÿ<-ÿF1)ÿ(v5-v7ÿ<-ÿF2)ÿ(v8-v10ÿ<-ÿF3)ÿ(F1ÿF2ÿF3ÿ<-ÿF4)

Endogenousÿvariables

Measurement:ÿÿv1ÿv2ÿv3ÿv4ÿv5ÿv6ÿv7ÿv8ÿv9ÿv10
Latent:ÿÿÿÿÿÿÿF1ÿF2ÿF3

Exogenousÿvariables

Latent:ÿÿÿÿÿÿÿF4

Fittingÿtargetÿmodel:

Iterationÿ0:ÿÿÿlogÿlikelihoodÿ=ÿ-1146.8738ÿÿ(notÿconcave)
Iterationÿ1:ÿÿÿlogÿlikelihoodÿ=ÿÿ-1135.332ÿÿ(notÿconcave)
Iterationÿ2:ÿÿÿlogÿlikelihoodÿ=ÿ-1107.9235ÿÿ(notÿconcave)
Iterationÿ3:ÿÿÿlogÿlikelihoodÿ=ÿ-1107.2526ÿÿ(notÿconcave)
Iterationÿ4:ÿÿÿlogÿlikelihoodÿ=ÿÿ-1106.984ÿÿ(notÿconcave)
Iterationÿ5:ÿÿÿlogÿlikelihoodÿ=ÿ-1106.8766ÿÿ(notÿconcave)
Iterationÿ6:ÿÿÿlogÿlikelihoodÿ=ÿ-1106.8551ÿÿ(notÿconcave)
Iterationÿ7:ÿÿÿlogÿlikelihoodÿ=ÿ-1106.8508ÿÿ(notÿconcave)
Iterationÿ8:ÿÿÿlogÿlikelihoodÿ=ÿ-1106.8491ÿÿ(notÿconcave)
Iterationÿ9:ÿÿÿlogÿlikelihoodÿ=ÿÿ-1106.849ÿÿ(notÿconcave)
Iterationÿ10:ÿÿlogÿlikelihoodÿ=ÿÿ-1106.849ÿÿ(notÿconcave)
Iterationÿ11:ÿÿlogÿlikelihoodÿ=ÿÿ-1106.849ÿÿ(notÿconcave)
Iterationÿ12:ÿÿlogÿlikelihoodÿ=ÿÿ-1106.849ÿÿ(notÿconcave)
Iterationÿ13:ÿÿlogÿlikelihoodÿ=ÿÿ-1106.849ÿÿ(notÿconcave)
Iterationÿ14:ÿÿlogÿlikelihoodÿ=ÿÿ-1106.849ÿÿ(notÿconcave)
Iterationÿ15:ÿÿlogÿlikelihoodÿ=ÿÿ-1106.849ÿÿ(notÿconcave)
Iterationÿ16:ÿÿlogÿlikelihoodÿ=ÿÿ-1106.849ÿÿ(notÿconcave)
Iterationÿ17:ÿÿlogÿlikelihoodÿ=ÿÿ-1106.849ÿÿ(notÿconcave)
Iterationÿ18:ÿÿlogÿlikelihoodÿ=ÿÿ-1106.849ÿÿ(notÿconcave)
Iterationÿ19:ÿÿlogÿlikelihoodÿ=ÿÿ-1106.849ÿÿ(notÿconcave)
Iterationÿ20:ÿÿlogÿlikelihoodÿ=ÿÿ-1106.849ÿÿ(notÿconcave)
Iterationÿ21:ÿÿlogÿlikelihoodÿ=ÿÿ-1106.849ÿÿ(notÿconcave)
Iterationÿ22:ÿÿlogÿlikelihoodÿ=ÿÿ-1106.849ÿÿ(notÿconcave)
Iterationÿ23:ÿÿlogÿlikelihoodÿ=ÿÿ-1106.849ÿÿ(notÿconcave)
Iterationÿ24:ÿÿlogÿlikelihoodÿ=ÿÿ-1106.849ÿÿ(notÿconcave)
Iterationÿ25:ÿÿlogÿlikelihoodÿ=ÿÿ-1106.849ÿÿ(notÿconcave)
Iterationÿ26:ÿÿlogÿlikelihoodÿ=ÿÿ-1106.849ÿÿ(notÿconcave)
Iterationÿ27:ÿÿlogÿlikelihoodÿ=ÿÿ-1106.849ÿÿ(notÿconcave)
Iterationÿ28:ÿÿlogÿlikelihoodÿ=ÿÿ-1106.849ÿÿ(notÿconcave)
--Break--
r(1);

endÿofÿdo-file

--Break--
r(1);

.

The scale reliability coefficient is so high (0.96) that many researchers would consider that they've just got a bunch of redundant items on a unidimensional scale that they ought to cull. I don't find your troubles at all surprising.
1 like
Comment
Joseph Coveney

Join Date: Apr 2014

Posts: 4375
#8

10 Feb 2021, 21:01

Maybe it will help to make sense out of it if you look at it as having too many estimates in your structural model chasing after too few actual unique parameters in the latent structure of the data to make estimates of. There are an infinite number of combinations of factor loadings and variances of the four latent factors that will fit equally well to the one simple covariance in the data. The likelihood (objective function) surface is going to have a huge equi-likelihood plateau that the maximization algorithm will wander around on in circles.

You can kind of fit your second-order model by handling the three scales separately in the three first-order latent factors, along with fitting covariances between the three. And then using that fitted model’s coefficients as constraints (there’s no other way for your model to find anything unique among the items) in a follow-on “locked-down” model, where you basically exchange your three factor loadings for the covariance terms. I show that below, but I wouldn’t bet the farm on such a jerry-rigged construction.

.ÿ
.ÿversionÿ16.1

.ÿ
.ÿclearÿ*

.ÿ
.ÿquietlyÿinputÿbyte(revrr_favorsÿrevrr_tryharder)ÿlong(rr_slaveryÿrr_deserve)ÿ///
>ÿÿÿÿÿÿÿÿÿbyteÿracineq_discrimÿlong(disc_blacksÿnodisc_equalincomesÿwpa_advantagesÿ///
>ÿÿÿÿÿÿÿÿÿwpa_opensdoorsÿwpa_easier)ÿbyteÿwhite

.ÿquietlyÿcompress

.ÿ
.ÿ*
.ÿ*ÿCovarianceÿfittedÿtoÿthreeÿfirst-orderÿfactors
.ÿ*
.ÿsemÿ///
>ÿÿÿÿÿÿÿÿÿ(revrr_favorsÿrevrr_tryharderÿrr_slaveryÿrr_deserveÿ<-ÿRR)ÿ///
>ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ(racineq_discrimÿdisc_blacksÿnodisc_equalincomesÿ<-ÿDISC)ÿ///
>ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ(wpa_advantages-wpa_easierÿ<-ÿWPA),ÿ///
>ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿmethod(adf)ÿ///
>ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿnocnsreportÿnodescribeÿnolog

Fittingÿbaselineÿmodel:

Iterationÿ0:ÿÿÿdiscrepancyÿ=ÿÿ898.81599ÿÿ
Iterationÿ1:ÿÿÿdiscrepancyÿ=ÿÿ4.0520075ÿÿ
Iterationÿ2:ÿÿÿdiscrepancyÿ=ÿÿ4.0520075ÿÿ(backedÿup)

StructuralÿequationÿmodelÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿNumberÿofÿobsÿÿÿÿÿ=ÿÿÿÿÿÿÿÿ100
Estimationÿmethodÿÿ=ÿadf
Discrepancyÿÿÿÿÿÿÿÿ=ÿÿ.57808747

-------------------------------------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ|ÿÿÿÿÿÿCoef.ÿÿÿStd.ÿErr.ÿÿÿÿÿÿzÿÿÿÿP>|z|ÿÿÿÿÿ[95%ÿConf.ÿInterval]
--------------------------+----------------------------------------------------------------
Measurementÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿrevrr_favorsÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿRRÿ|ÿÿÿÿÿÿÿÿÿÿ1ÿÿ(constrained)
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ_consÿ|ÿÿÿ3.656492ÿÿÿ.1137552ÿÿÿÿ32.14ÿÿÿ0.000ÿÿÿÿÿ3.433536ÿÿÿÿ3.879448
ÿÿ------------------------+----------------------------------------------------------------
ÿÿrevrr_tryharderÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿRRÿ|ÿÿÿ.8409892ÿÿÿ.0455616ÿÿÿÿ18.46ÿÿÿ0.000ÿÿÿÿÿÿÿ.75169ÿÿÿÿ.9302884
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ_consÿ|ÿÿÿ4.031682ÿÿÿ.1039593ÿÿÿÿ38.78ÿÿÿ0.000ÿÿÿÿÿ3.827925ÿÿÿÿ4.235438
ÿÿ------------------------+----------------------------------------------------------------
ÿÿrr_slaveryÿÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿRRÿ|ÿÿÿÿ.702112ÿÿÿ.0651877ÿÿÿÿ10.77ÿÿÿ0.000ÿÿÿÿÿ.5743464ÿÿÿÿ.8298775
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ_consÿ|ÿÿÿ3.952307ÿÿÿ.1181395ÿÿÿÿ33.45ÿÿÿ0.000ÿÿÿÿÿ3.720758ÿÿÿÿ4.183856
ÿÿ------------------------+----------------------------------------------------------------
ÿÿrr_deserveÿÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿRRÿ|ÿÿÿ.9471143ÿÿÿ.0393674ÿÿÿÿ24.06ÿÿÿ0.000ÿÿÿÿÿ.8699556ÿÿÿÿ1.024273
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ_consÿ|ÿÿÿ3.826854ÿÿÿ.1063248ÿÿÿÿ35.99ÿÿÿ0.000ÿÿÿÿÿ3.618461ÿÿÿÿ4.035247
ÿÿ------------------------+----------------------------------------------------------------
ÿÿracineq_discrimÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿDISCÿ|ÿÿÿÿÿÿÿÿÿÿ1ÿÿ(constrained)
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ_consÿ|ÿÿÿ65.68267ÿÿÿ2.610211ÿÿÿÿ25.16ÿÿÿ0.000ÿÿÿÿÿ60.56675ÿÿÿÿ70.79859
ÿÿ------------------------+----------------------------------------------------------------
ÿÿdisc_blacksÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿDISCÿ|ÿÿÿ.0359937ÿÿÿ.0020285ÿÿÿÿ17.74ÿÿÿ0.000ÿÿÿÿÿ.0320179ÿÿÿÿ.0399695
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ_consÿ|ÿÿÿ3.971693ÿÿÿ.0998203ÿÿÿÿ39.79ÿÿÿ0.000ÿÿÿÿÿ3.776049ÿÿÿÿ4.167338
ÿÿ------------------------+----------------------------------------------------------------
ÿÿnodisc_equalincomesÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿDISCÿ|ÿÿÿ.0457124ÿÿÿ.0038569ÿÿÿÿ11.85ÿÿÿ0.000ÿÿÿÿÿ.0381531ÿÿÿÿ.0532718
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ_consÿ|ÿÿÿ4.778216ÿÿÿ.1432288ÿÿÿÿ33.36ÿÿÿ0.000ÿÿÿÿÿ4.497493ÿÿÿÿÿ5.05894
ÿÿ------------------------+----------------------------------------------------------------
ÿÿwpa_advantagesÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿWPAÿ|ÿÿÿÿÿÿÿÿÿÿ1ÿÿ(constrained)
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ_consÿ|ÿÿÿ5.462988ÿÿÿ.1574787ÿÿÿÿ34.69ÿÿÿ0.000ÿÿÿÿÿ5.154336ÿÿÿÿ5.771641
ÿÿ------------------------+----------------------------------------------------------------
ÿÿwpa_opensdoorsÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿWPAÿ|ÿÿÿ1.065464ÿÿÿ.0279471ÿÿÿÿ38.12ÿÿÿ0.000ÿÿÿÿÿ1.010689ÿÿÿÿ1.120239
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ_consÿ|ÿÿÿ5.267212ÿÿÿ.1552016ÿÿÿÿ33.94ÿÿÿ0.000ÿÿÿÿÿ4.963023ÿÿÿÿ5.571402
ÿÿ------------------------+----------------------------------------------------------------
ÿÿwpa_easierÿÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿWPAÿ|ÿÿÿ1.089887ÿÿÿ.0227654ÿÿÿÿ47.87ÿÿÿ0.000ÿÿÿÿÿ1.045268ÿÿÿÿ1.134507
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ_consÿ|ÿÿÿ5.383029ÿÿÿ.1603893ÿÿÿÿ33.56ÿÿÿ0.000ÿÿÿÿÿ5.068672ÿÿÿÿ5.697386
--------------------------+----------------------------------------------------------------
ÿÿÿÿÿÿÿvar(e.revrr_favors)|ÿÿÿ.2909086ÿÿÿ.0588489ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.1956879ÿÿÿÿ.4324631
ÿÿÿÿvar(e.revrr_tryharder)|ÿÿÿ.2047126ÿÿÿ.0570692ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.1185356ÿÿÿÿ.3535412
ÿÿÿÿÿÿÿÿÿvar(e.rr_slavery)|ÿÿÿ1.114005ÿÿÿ.1621271ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.8375428ÿÿÿÿ1.481723
ÿÿÿÿÿÿÿÿÿvar(e.rr_deserve)|ÿÿÿ.2159436ÿÿÿÿ.063992ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.1208087ÿÿÿÿ.3859956
ÿÿÿÿvar(e.racineq_discrim)|ÿÿÿ121.8929ÿÿÿÿ33.4578ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ71.17647ÿÿÿÿ208.7472
ÿÿÿÿÿÿÿÿvar(e.disc_blacks)|ÿÿÿ.2729104ÿÿÿ.0285414ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.222331ÿÿÿÿ.3349963
var(e.nodisc_equalincomes)|ÿÿÿ.9500545ÿÿÿ.1311017ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.7249164ÿÿÿÿ1.245114
ÿÿÿÿÿvar(e.wpa_advantages)|ÿÿÿ.0796972ÿÿÿ.0332432ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.0351876ÿÿÿÿ.1805077
ÿÿÿÿÿvar(e.wpa_opensdoors)|ÿÿÿ.1513396ÿÿÿ.0731341ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.0586967ÿÿÿÿ.3902035
ÿÿÿÿÿÿÿÿÿvar(e.wpa_easier)|ÿÿÿ.1552586ÿÿÿÿ.054459ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.0780703ÿÿÿÿ.3087633
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿvar(RR)|ÿÿÿÿ1.89611ÿÿÿ.1510682ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ1.621982ÿÿÿÿ2.216568
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿvar(DISC)|ÿÿÿ843.0252ÿÿÿ89.73492ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ684.2823ÿÿÿÿ1038.594
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿvar(WPA)|ÿÿÿ3.754846ÿÿÿÿ.398647ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ3.049448ÿÿÿÿ4.623417
--------------------------+----------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿcov(RR,DISC)|ÿÿÿ40.10259ÿÿÿ3.281377ÿÿÿÿ12.22ÿÿÿ0.000ÿÿÿÿÿ33.67121ÿÿÿÿ46.53397
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿcov(RR,WPA)|ÿÿÿ2.543052ÿÿÿ.2265508ÿÿÿÿ11.23ÿÿÿ0.000ÿÿÿÿÿ2.099021ÿÿÿÿ2.987083
ÿÿÿÿÿÿÿÿÿÿÿÿÿcov(DISC,WPA)|ÿÿÿ55.44576ÿÿÿÿ5.47655ÿÿÿÿ10.12ÿÿÿ0.000ÿÿÿÿÿ44.71192ÿÿÿÿÿ66.1796
-------------------------------------------------------------------------------------------
Discr.ÿtestÿofÿmodelÿvs.ÿsaturated:ÿchi2(32)ÿÿ=ÿÿÿÿ57.81,ÿProbÿ>ÿchi2ÿ=ÿ0.0034

.ÿ
.ÿ*
.ÿ*ÿForce-fitÿyourÿsecond-orderÿfactorÿmodel
.ÿ*
.ÿtempnameÿB

.ÿmatrixÿdefineÿ`B'ÿ=ÿe(b)

.ÿlocalÿcolsÿ:ÿcolfullnamesÿ`B'

.ÿlocalÿcolnumÿ:ÿcolsofÿ`B'

.ÿlocalÿiÿ1

.ÿforeachÿcolÿofÿlocalÿcolsÿ{
ÿÿ2.ÿ
.ÿÿÿÿÿÿÿÿÿ//ÿFirst-orderÿfactorsÿnowÿbecomeÿendogenousÿ(i.e.,ÿwithÿerrorÿvariance)
.ÿÿÿÿÿÿÿÿÿifÿinlist("`col'",ÿ"/var(RR)",ÿ"/var(DISC)",ÿ"/var(WPA)")ÿ///
>ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿlocalÿcolÿ:ÿsubinstrÿlocalÿcolÿ"/var("ÿ"/var(e."
ÿÿ3.ÿ
.ÿÿÿÿÿÿÿÿÿ//ÿRemoveÿcovarianceÿtermsÿbetweenÿlatentÿfactors
.ÿÿÿÿÿÿÿÿÿifÿ(`colnum'ÿ-ÿ3)ÿ<ÿ`i'ÿcontinue,ÿbreak
ÿÿ4.ÿ
.ÿÿÿÿÿÿÿÿÿconstraintÿdefineÿ`i'ÿ_b[`col']ÿ=ÿ`B'[1,ÿ`i']
ÿÿ5.ÿÿÿÿÿÿÿÿÿlocalÿ++i
ÿÿ6.ÿ}

.ÿ
.ÿsemÿ///
>ÿÿÿÿÿÿÿÿÿ(revrr_favorsÿrevrr_tryharderÿrr_slaveryÿrr_deserveÿ<-ÿRR)ÿ///
>ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ(racineq_discrimÿdisc_blacksÿnodisc_equalincomesÿ<-ÿDISC)ÿ///
>ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ(wpa_advantages-wpa_easierÿ<-ÿWPA)ÿ///
>ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ(RRÿDISCÿWPAÿ<-ÿGF),ÿvariance(GF@1)ÿ///
>ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿmethod(adf)ÿconstraints(1/`=`i'-1')ÿ///
>ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿnocnsreportÿnodescribeÿnolog

Fittingÿbaselineÿmodel:

Iterationÿ0:ÿÿÿdiscrepancyÿ=ÿÿ898.81599ÿÿ
Iterationÿ1:ÿÿÿdiscrepancyÿ=ÿÿ4.0520075ÿÿ
Iterationÿ2:ÿÿÿdiscrepancyÿ=ÿÿ4.0520075ÿÿ(backedÿup)

StructuralÿequationÿmodelÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿNumberÿofÿobsÿÿÿÿÿ=ÿÿÿÿÿÿÿÿ100
Estimationÿmethodÿÿ=ÿadf
Discrepancyÿÿÿÿÿÿÿÿ=ÿÿ508.29384

-------------------------------------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ|ÿÿÿÿÿÿCoef.ÿÿÿStd.ÿErr.ÿÿÿÿÿÿzÿÿÿÿP>|z|ÿÿÿÿÿ[95%ÿConf.ÿInterval]
--------------------------+----------------------------------------------------------------
Structuralÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿRRÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿGFÿ|ÿÿÿ.7804523ÿÿÿ.0257447ÿÿÿÿ30.32ÿÿÿ0.000ÿÿÿÿÿ.7299936ÿÿÿÿÿ.830911
ÿÿ------------------------+----------------------------------------------------------------
ÿÿDISCÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿGFÿ|ÿÿÿ14.12616ÿÿÿ.4786076ÿÿÿÿ29.52ÿÿÿ0.000ÿÿÿÿÿÿ13.1881ÿÿÿÿ15.06421
ÿÿ------------------------+----------------------------------------------------------------
ÿÿWPAÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿGFÿ|ÿÿÿ1.248172ÿÿÿÿ.040204ÿÿÿÿ31.05ÿÿÿ0.000ÿÿÿÿÿ1.169373ÿÿÿÿÿ1.32697
--------------------------+----------------------------------------------------------------
Measurementÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿrevrr_favorsÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿRRÿ|ÿÿÿÿÿÿÿÿÿÿ1ÿÿ(constrained)
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ_consÿ|ÿÿÿ3.656492ÿÿ(constrained)
ÿÿ------------------------+----------------------------------------------------------------
ÿÿrevrr_tryharderÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿRRÿ|ÿÿÿ.8409892ÿÿ(constrained)
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ_consÿ|ÿÿÿ4.031682ÿÿ(constrained)
ÿÿ------------------------+----------------------------------------------------------------
ÿÿrr_slaveryÿÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿRRÿ|ÿÿÿÿ.702112ÿÿ(constrained)
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ_consÿ|ÿÿÿ3.952307ÿÿ(constrained)
ÿÿ------------------------+----------------------------------------------------------------
ÿÿrr_deserveÿÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿRRÿ|ÿÿÿ.9471143ÿÿ(constrained)
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ_consÿ|ÿÿÿ3.826854ÿÿ(constrained)
ÿÿ------------------------+----------------------------------------------------------------
ÿÿracineq_discrimÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿDISCÿ|ÿÿÿÿÿÿÿÿÿÿ1ÿÿ(constrained)
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ_consÿ|ÿÿÿ65.68267ÿÿ(constrained)
ÿÿ------------------------+----------------------------------------------------------------
ÿÿdisc_blacksÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿDISCÿ|ÿÿÿ.0359937ÿÿ(constrained)
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ_consÿ|ÿÿÿ3.971693ÿÿ(constrained)
ÿÿ------------------------+----------------------------------------------------------------
ÿÿnodisc_equalincomesÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿDISCÿ|ÿÿÿ.0457124ÿÿ(constrained)
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ_consÿ|ÿÿÿ4.778216ÿÿ(constrained)
ÿÿ------------------------+----------------------------------------------------------------
ÿÿwpa_advantagesÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿWPAÿ|ÿÿÿÿÿÿÿÿÿÿ1ÿÿ(constrained)
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ_consÿ|ÿÿÿ5.462988ÿÿ(constrained)
ÿÿ------------------------+----------------------------------------------------------------
ÿÿwpa_opensdoorsÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿWPAÿ|ÿÿÿ1.065464ÿÿ(constrained)
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ_consÿ|ÿÿÿ5.267212ÿÿ(constrained)
ÿÿ------------------------+----------------------------------------------------------------
ÿÿwpa_easierÿÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿWPAÿ|ÿÿÿ1.089887ÿÿ(constrained)
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ_consÿ|ÿÿÿ5.383029ÿÿ(constrained)
--------------------------+----------------------------------------------------------------
ÿÿÿÿÿÿÿvar(e.revrr_favors)|ÿÿÿ.2909086ÿÿ(constrained)
ÿÿÿÿvar(e.revrr_tryharder)|ÿÿÿ.2047126ÿÿ(constrained)
ÿÿÿÿÿÿÿÿÿvar(e.rr_slavery)|ÿÿÿ1.114005ÿÿ(constrained)
ÿÿÿÿÿÿÿÿÿvar(e.rr_deserve)|ÿÿÿ.2159436ÿÿ(constrained)
ÿÿÿÿvar(e.racineq_discrim)|ÿÿÿ121.8929ÿÿ(constrained)
ÿÿÿÿÿÿÿÿvar(e.disc_blacks)|ÿÿÿ.2729104ÿÿ(constrained)
var(e.nodisc_equalincomes)|ÿÿÿ.9500545ÿÿ(constrained)
ÿÿÿÿÿvar(e.wpa_advantages)|ÿÿÿ.0796972ÿÿ(constrained)
ÿÿÿÿÿvar(e.wpa_opensdoors)|ÿÿÿ.1513396ÿÿ(constrained)
ÿÿÿÿÿÿÿÿÿvar(e.wpa_easier)|ÿÿÿ.1552586ÿÿ(constrained)
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿvar(e.RR)|ÿÿÿÿ1.89611ÿÿ(constrained)
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿvar(e.DISC)|ÿÿÿ843.0252ÿÿ(constrained)
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿvar(e.WPA)|ÿÿÿ3.754846ÿÿ(constrained)
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿvar(GF)|ÿÿÿÿÿÿÿÿÿÿ1ÿÿ(constrained)
-------------------------------------------------------------------------------------------
Discr.ÿtestÿofÿmodelÿvs.ÿsaturated:ÿchi2(62)ÿÿ=ÿ50829.38,ÿProbÿ>ÿchi2ÿ=ÿ0.0000

.ÿ
.ÿexit

endÿofÿdo-file

.
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Announcement

SEM CFA with higher-order factor not converging

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