Figure with hypothesized correlations on left and actual correlations on right

[Chris Martin]

I created a new psychological scale to measure a construct and I hypothesized the correlations it would have with related constructs. I'd now like to generate something like the figure below which from Costello et al. (2020), Clarifying the structure and nature of left-wing authoritarianism.

The hypothesized correlations are on the left and the actual ones are on the right. I want just one box on the right, not two as shown here. I know that coefplot can create graphs from regressions like this, but I don't think it works with correlations. And I don't think you can create a layout with a hypothesized set of correlations on the left. (I believe R was used to generate this one.) Is this doable in Stata?

[Andrew Musau]

I created a new psychological scale to measure a construct and I hypothesized the correlations it would have with related constructs.

Provide us a sample of such correlations.

[Chris Martin]

Here is some data for the correlations

* Example generated by -dataex-. For more info, type help dataex
clear
input float(sjtsima ang del emp frk honeshex npow ih jsb jso clos sdo tru)
25  1.4  3.777778 3.9 4.875 4.3125  3.666667  4.681818   2   3       2.4     3  2.909091
18 2.75         3 3.9 3.125 3.4375         3 3.5454545 4.5 4.5       4.6  2.25 2.3636363
25    2  3.777778 4.1 2.875 3.1875  3.142857  3.636364   3 3.5       4.8   1.5  2.818182
25  2.1  4.111111   4 3.375  3.875 2.2857144  3.909091 3.5 2.5 3.8666666 2.125  2.636364
24  1.1         4   4  3.25 4.3125  3.857143 4.2272725 4.5   5         2     1         4
24  1.8         4 4.1 3.875 4.0625 2.5714285 4.1363635   2   3 3.8666666 2.875  3.727273
21  2.2  4.111111 3.3   3.5 4.1875 1.8571428 3.5454545   4   4  5.133333     1         4
25  1.1 4.3333335 4.9 2.375    4.5 2.4285715 4.4545455 4.5 3.5 2.3333333 1.375 4.4545455
25  2.2         4 3.9 2.125 3.6875  3.142857 3.4545455   4   4  4.933333 4.125  3.818182
19  2.1 4.4444447 4.6  3.25 3.9375         3 4.0454545   3   3  4.733333 2.125  3.272727
20    2         4   4  3.75    3.5         3 3.5454545   2   3         5   3.5  2.909091
19  2.4 3.5555556 3.5  2.25 3.8125 1.7142857  3.636364   3   3  4.866667  3.25         3
18  2.6  3.888889 3.7 2.625 3.1875 3.2857144  3.318182   3   3       4.6     4 2.5454545
21  2.2 3.5555556 3.9     4 3.9375 3.2857144 4.1363635   1   1  3.533333 3.375 4.4545455
20  2.2  4.111111 3.5 4.125  2.625 2.7142856  3.181818   5 4.5  5.533333  1.75  3.090909
end

The key variable is sjtsima.

To get the actual correlations, see the first column:

pwcorr sjtsima ang del emp frk hon npow ih jsb jso clos sdo tru

Here are the hypothesized correlations in the same order as listed above from ang through tru:

Anger Proneness (Neuro. facet) -0.10
Deliberation (Consc. facet) 0
Empathy (Agree. facet) 0.35
Frankness (Extra. facet) 0.10
Honesty-humility 0.20
nPow: Implicit need for power -0.25
Intellectual Humility 0.20
Justice sensitivity (Beneficiary) 0.35
Justice Sensitivity (Observer) 0.30
Closure: i.e. Need for closure -0.15
Social Dominance Orientation -0.30
Trust (Agree.facet) 0.25

Thanks!

[Andrew Musau]

Thanks. I use coefplot from SSC. You can further customize the graph using standard twoway options.

clear
input float(sjtsima ang del emp frk honeshex npow ih jsb jso clos sdo tru)
25  1.4  3.777778 3.9 4.875 4.3125  3.666667  4.681818   2   3       2.4     3  2.909091
18 2.75         3 3.9 3.125 3.4375         3 3.5454545 4.5 4.5       4.6  2.25 2.3636363
25    2  3.777778 4.1 2.875 3.1875  3.142857  3.636364   3 3.5       4.8   1.5  2.818182
25  2.1  4.111111   4 3.375  3.875 2.2857144  3.909091 3.5 2.5 3.8666666 2.125  2.636364
24  1.1         4   4  3.25 4.3125  3.857143 4.2272725 4.5   5         2     1         4
24  1.8         4 4.1 3.875 4.0625 2.5714285 4.1363635   2   3 3.8666666 2.875  3.727273
21  2.2  4.111111 3.3   3.5 4.1875 1.8571428 3.5454545   4   4  5.133333     1         4
25  1.1 4.3333335 4.9 2.375    4.5 2.4285715 4.4545455 4.5 3.5 2.3333333 1.375 4.4545455
25  2.2         4 3.9 2.125 3.6875  3.142857 3.4545455   4   4  4.933333 4.125  3.818182
19  2.1 4.4444447 4.6  3.25 3.9375         3 4.0454545   3   3  4.733333 2.125  3.272727
20    2         4   4  3.75    3.5         3 3.5454545   2   3         5   3.5  2.909091
19  2.4 3.5555556 3.5  2.25 3.8125 1.7142857  3.636364   3   3  4.866667  3.25         3
18  2.6  3.888889 3.7 2.625 3.1875 3.2857144  3.318182   3   3       4.6     4 2.5454545
21  2.2 3.5555556 3.9     4 3.9375 3.2857144 4.1363635   1   1  3.533333 3.375 4.4545455
20  2.2  4.111111 3.5 4.125  2.625 2.7142856  3.181818   5 4.5  5.533333  1.75  3.090909
end

cap frame drop corr
frame create corr
frame corr{
    clear
    input str400 label str10 var float corr2
    "Anger Proneness (Neuro. facet)" "ang" -0.10
    "Deliberation (Consc. facet)" "del" 0
    "Empathy (Agree. facet)" "emp" 0.35
    "Frankness (Extra. facet)" "frk" 0.10
    "Honesty-humility" "honeshex" 0.20
    "nPow: Implicit need for power" "npow" -0.25
    "Intellectual Humility" "ih" 0.20
    "Justice sensitivity (Benefic.)" "jsb" 0.35
    "Justice Sensitivity (Observer)" "jso" 0.30
    "Closure: i.e. Need for closure" "clos" -0.15
    "Social Dominance Orientation" "sdo" -0.30
    "Trust (Agree. facet)" "tru" 0.25
    end
    gen corr=.
    replace label= ustrregexra(subinstr(trim(itrim(label)), ".", "", .), "[\s]", "`=uchar(160)'")
}

foreach var of varlist ang-tru{
    corr sjtsima `var'
    frame corr: replace corr= r(rho) if var=="`var'"
}


frame corr: mkmat corr, mat(Actual) rownames(var) roweq(label)
frame corr: mkmat corr2, mat(Predicted) rownames(var) roweq(label)

coefplot matrix(Actual[,1])|| matrix(Predicted[,1])||, keep(*:) ylab("")

[Nick Cox]

I would tend to prefer correlations being superimposed. It's a little awkward to have predicted correlations in the same dataset as the data, but it's perfectly possible. Following Andrew Musau's lead consider something like this:

clear
input float(sjtsima ang del emp frk honeshex npow ih jsb jso clos sdo tru)
25  1.4  3.777778 3.9 4.875 4.3125  3.666667  4.681818   2   3       2.4     3  2.909091
18 2.75         3 3.9 3.125 3.4375         3 3.5454545 4.5 4.5       4.6  2.25 2.3636363
25    2  3.777778 4.1 2.875 3.1875  3.142857  3.636364   3 3.5       4.8   1.5  2.818182
25  2.1  4.111111   4 3.375  3.875 2.2857144  3.909091 3.5 2.5 3.8666666 2.125  2.636364
24  1.1         4   4  3.25 4.3125  3.857143 4.2272725 4.5   5         2     1         4
24  1.8         4 4.1 3.875 4.0625 2.5714285 4.1363635   2   3 3.8666666 2.875  3.727273
21  2.2  4.111111 3.3   3.5 4.1875 1.8571428 3.5454545   4   4  5.133333     1         4
25  1.1 4.3333335 4.9 2.375    4.5 2.4285715 4.4545455 4.5 3.5 2.3333333 1.375 4.4545455
25  2.2         4 3.9 2.125 3.6875  3.142857 3.4545455   4   4  4.933333 4.125  3.818182
19  2.1 4.4444447 4.6  3.25 3.9375         3 4.0454545   3   3  4.733333 2.125  3.272727
20    2         4   4  3.75    3.5         3 3.5454545   2   3         5   3.5  2.909091
19  2.4 3.5555556 3.5  2.25 3.8125 1.7142857  3.636364   3   3  4.866667  3.25         3
18  2.6  3.888889 3.7 2.625 3.1875 3.2857144  3.318182   3   3       4.6     4 2.5454545
21  2.2 3.5555556 3.9     4 3.9375 3.2857144 4.1363635   1   1  3.533333 3.375 4.4545455
20  2.2  4.111111 3.5 4.125  2.625 2.7142856  3.181818   5 4.5  5.533333  1.75  3.090909
end

input str400 label str10 var float corr2
    "Anger Proneness (Neuro. facet)" "ang" -0.10
    "Deliberation (Consc. facet)" "del" 0
    "Empathy (Agree. facet)" "emp" 0.35
    "Frankness (Extra. facet)" "frk" 0.10
    "Honesty-humility" "honeshex" 0.20
    "nPow: Implicit need for power" "npow" -0.25
    "Intellectual Humility" "ih" 0.20
    "Justice sensitivity (Benefic.)" "jsb" 0.35
    "Justice Sensitivity (Observer)" "jso" 0.30
    "Closure: i.e. Need for closure" "clos" -0.15
    "Social Dominance Orientation" "sdo" -0.30
    "Trust (Agree. facet)" "tru" 0.25
end
    
gen corr=.

foreach var of varlist ang-tru{
    corr sjtsima `var'
    replace corr= r(rho) if var=="`var'"
}

graph dot (asis) corr corr2 , over(label, sort(corr)) marker(1, ms(Oh) msize(*2)) marker(2, ms(+) msize(*2)) legend(order(1 "observed" 2 "predicted") row(1) pos(6)) yscale(alt) t1title(Observed and predicted correlations) linetype(line) lines(lc(gs12) lw(vthin))

[Chris Martin]

Thank you. I like the use of a single graph. Is there a way to add the 95% confidence intervals?

[Andrew Musau]

For the Pearson correlation coefficients, you could, for example, use bootstrapping to obtain the confidence intervals. For your own results, you'll need to provide these yourself.

clear
input float(sjtsima ang del emp frk honeshex npow ih jsb jso clos sdo tru)
25  1.4  3.777778 3.9 4.875 4.3125  3.666667  4.681818   2   3       2.4     3  2.909091
18 2.75         3 3.9 3.125 3.4375         3 3.5454545 4.5 4.5       4.6  2.25 2.3636363
25    2  3.777778 4.1 2.875 3.1875  3.142857  3.636364   3 3.5       4.8   1.5  2.818182
25  2.1  4.111111   4 3.375  3.875 2.2857144  3.909091 3.5 2.5 3.8666666 2.125  2.636364
24  1.1         4   4  3.25 4.3125  3.857143 4.2272725 4.5   5         2     1         4
24  1.8         4 4.1 3.875 4.0625 2.5714285 4.1363635   2   3 3.8666666 2.875  3.727273
21  2.2  4.111111 3.3   3.5 4.1875 1.8571428 3.5454545   4   4  5.133333     1         4
25  1.1 4.3333335 4.9 2.375    4.5 2.4285715 4.4545455 4.5 3.5 2.3333333 1.375 4.4545455
25  2.2         4 3.9 2.125 3.6875  3.142857 3.4545455   4   4  4.933333 4.125  3.818182
19  2.1 4.4444447 4.6  3.25 3.9375         3 4.0454545   3   3  4.733333 2.125  3.272727
20    2         4   4  3.75    3.5         3 3.5454545   2   3         5   3.5  2.909091
19  2.4 3.5555556 3.5  2.25 3.8125 1.7142857  3.636364   3   3  4.866667  3.25         3
18  2.6  3.888889 3.7 2.625 3.1875 3.2857144  3.318182   3   3       4.6     4 2.5454545
21  2.2 3.5555556 3.9     4 3.9375 3.2857144 4.1363635   1   1  3.533333 3.375 4.4545455
20  2.2  4.111111 3.5 4.125  2.625 2.7142856  3.181818   5 4.5  5.533333  1.75  3.090909
end

cap frame drop corr
frame create corr
frame corr{
    clear
    input str400 label str10 var float corr2
    "Anger Proneness (Neuro. facet)" "ang" -0.10
    "Deliberation (Consc. facet)" "del" 0
    "Empathy (Agree. facet)" "emp" 0.35
    "Frankness (Extra. facet)" "frk" 0.10
    "Honesty-humility" "honeshex" 0.20
    "nPow: Implicit need for power" "npow" -0.25
    "Intellectual Humility" "ih" 0.20
    "Justice sensitivity (Benefic.)" "jsb" 0.35
    "Justice Sensitivity (Observer)" "jso" 0.30
    "Closure: i.e. Need for closure" "clos" -0.15
    "Social Dominance Orientation" "sdo" -0.30
    "Trust (Agree. facet)" "tru" 0.25
    end
    gen corr=.
    gen ll=.
    gen ul=.
    replace label= ustrregexra(trim(itrim(label)), "[\s]", "`=uchar(160)'")
    replace label= ustrregexra(label, "[\.]", "`=ustrunescape("\u2024")'")
    replace label= ustrregexra(label, "[\:]", "`=ustrunescape("\uff1a")'")
}
set seed 04242025
foreach var of varlist ang-tru{
   bootstrap rho = r(rho), reps(400): corr sjtsima `var'
    frame corr: replace corr= r(table)["b", 1] if var=="`var'"
    frame corr: replace ll= r(table)["ll", 1] if var=="`var'"
    frame corr: replace ul= r(table)["ul", 1] if var=="`var'"
}

frame corr: sort corr
frame corr: mkmat corr ll ul, mat(Actual) rownames(var) roweq(label)
frame corr: mkmat corr2, mat(Hypothesized) rownames(var) roweq(label)

coefplot matrix(Hypothesized[,1])|| matrix(Actual[,1]), ci((Actual[,2] Actual[,3]))||, keep(*:) ///
nokey norecycle ylab("") b1title(Correlations) xline(0, lp(dash) lc(red))

[Chris Martin]

Thanks. This runs on my end, but the variables labels are vertically oriented instead of horizontally oriented. However this could be due to Stata 17. I am most of my work on a computer with Stata 19

[Andrew Musau]

I can replicate that in V16. You can add:

coefplot matrix(Hypothesized[,1])|| matrix(Actual[,1]), ci((Actual[,2] Actual[,3]))||, keep(*:) ///
nokey norecycle ylab("") eqlab(, angle(horiz)) b1title(Correlations) xline(0, lp(dash) lc(red))

[Chris Martin]

Thanks. I'm trying to sort the items on the y axis in alphabetical order by variable, which is: ang del emp frk honeshex npow ih jsb jso clos sdo tru.

However, the documentation for coefplot suggests that the sort option doesn't support this. Do you know of another way?

[Andrew Musau]

The sort command in #7 is:

frame corr: sort corr

Reading the graph is easier when the correlations are sorted, but the best way to get what you want is to order the variables before building the matrix.

order sjtsima ang del emp frk honeshex npow ih jsb jso clos sdo tru

foreach var of varlist ang-tru{
    bootstrap rho = r(rho), reps(400): corr sjtsima `var'
    frame corr: replace corr= r(table)["b", 1] if var=="`var'"
    frame corr: replace ll= r(table)["ll", 1] if var=="`var'"
    frame corr: replace ul= r(table)["ul", 1] if var=="`var'"
} 
frame corr: mkmat corr ll ul, mat(Actual) rownames(var) roweq(label)
frame corr: mkmat corr2, mat(Hypothesized) rownames(var) roweq(label)

coefplot matrix(Hypothesized[,1])|| matrix(Actual[,1]), ci((Actual[,2] Actual[,3]))||, keep(*:) ///
nokey norecycle ylab("") eqlab(,angle(horiz)) b1title(Correlations) xline(0, lp(dash) lc(red))