nlcom: maximum

[louisa linkemeyer]

Hello together,

we're doing an inverted u-shape analysis on the impact of CSR Score on the TOA of different firms moderated by our time invariant moderator Consistency (Kurtosis of CSR Score).
We would like to investigate if the turning point of the u-shape relationships significantly deviates with different levels of consistency. Therefore we found examples who used the nlcom code using the minimum, maximum, mean, mean +1 SD & mean - 1 SD levels of the moderating variables values.

We ran the following:

 xtreg roa c.csr_score##c.csr_score##c.consistency ln_firmsize ln_adi ln_rdi slack lev_w industry_growth industry
> _concentration i.fyear, fe cluster(cusipnr)
note: consistency omitted because of collinearity.

Fixed-effects (within) regression               Number of obs     =      4,417
Group variable: cusipnr                         Number of groups  =        606

R-squared:                                      Obs per group:
     Within  = 0.0754                                         min =          3
     Between = 0.0699                                         avg =        7.3
     Overall = 0.0472                                         max =         16

                                                F(26,605)         =       4.38
corr(u_i, Xb) = -0.3052                         Prob > F          =     0.0000

                                                       (Std. err. adjusted for 606 clusters in cusipnr)
-------------------------------------------------------------------------------------------------------
                                      |               Robust
                                  roa | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
--------------------------------------+----------------------------------------------------------------
                            csr_score |   .0017239   .0005557     3.10   0.002     .0006325    .0028154
                                      |
              c.csr_score#c.csr_score |   -.000018   5.19e-06    -3.46   0.001    -.0000282   -7.77e-06
                                      |
                          consistency |          0  (omitted)
                                      |
            c.csr_score#c.consistency |  -.0007174   .0002731    -2.63   0.009    -.0012538    -.000181
                                      |
c.csr_score#c.csr_score#c.consistency |   7.78e-06   2.65e-06     2.94   0.003     2.58e-06     .000013
                                      |
                          ln_firmsize |  -.0031383   .0062741    -0.50   0.617    -.0154599    .0091834
                               ln_adi |  -.0052481   .0055574    -0.94   0.345    -.0161622     .005666
                               ln_rdi |  -.0486486    .008962    -5.43   0.000     -.066249   -.0310483
                                slack |   -.116426   .0318931    -3.65   0.000    -.1790607   -.0537912
                                lev_w |   .0001744   .0007524     0.23   0.817    -.0013032     .001652
                      industry_growth |   .0262122   .0120354     2.18   0.030      .002576    .0498483
               industry_concentration |  -.0017947   .0170669    -0.11   0.916    -.0353123    .0317229
                                      |
                                fyear |
                                2004  |   .0264904   .0091348     2.90   0.004     .0085506    .0444301
                                2005  |   .0261167   .0113369     2.30   0.022     .0038522    .0483813
                                2006  |   .0290126   .0124341     2.33   0.020     .0045934    .0534318
                                2007  |   .0214981   .0125808     1.71   0.088    -.0032092    .0462054
                                2011  |   .0261853   .0138109     1.90   0.058     -.000938    .0533085
                                2012  |   .0136148   .0139187     0.98   0.328      -.01372    .0409495
                                2013  |   .0172718   .0141745     1.22   0.224    -.0105654    .0451089
                                2014  |   .0222723   .0142534     1.56   0.119    -.0057199    .0502645
                                2015  |   .0169446    .014851     1.14   0.254    -.0122211    .0461104
                                2016  |   .0195737   .0148799     1.32   0.189    -.0096489    .0487963
                                2017  |    .016874   .0156194     1.08   0.280    -.0138008    .0475488
                                2018  |   .0337998   .0159556     2.12   0.035     .0024647    .0651348
                                2019  |    .026212   .0169868     1.54   0.123    -.0071483    .0595723
                                2020  |   .0236843   .0181686     1.30   0.193     -.011997    .0593655
                                2021  |   .0459652   .0183655     2.50   0.013     .0098973     .082033
                                      |
                                _cons |  -.1923473    .059989    -3.21   0.001    -.3101592   -.0745354
--------------------------------------+----------------------------------------------------------------
                              sigma_u |  .13053874
                              sigma_e |  .08199672
                                  rho |  .71707153   (fraction of variance due to u_i)
-------------------------------------------------------------------------------------------------------

followed by the nlcom (-5.955 is the minimum of consistency)

nlcom (_b[csr_score]*_b[c.csr_score#c.csr_score#c.consistency] - _b[c.csr_score#c.csr_score]*_b[c.csr_score#c.co
> nsistency]) / 2*(_b[c.csr_score#c.csr_score]+_b[c.csr_score#c.csr_score#c.consistency]*(-5.954534))^2

We got the error "Maximum number of iterations exceeded." What can be the reasons for this error? Maybe because consistency got omitted in the regression? Or maybe because of our very low coefficients? How can we solve this problem?

Thank you for every little hint

[Joro Kolev]

For the reasons that you yourself mention, the fitted model does not look good at all: consistency is omitted, and the triple interaction has a coefficient very close to 0. Apparently this causes numerical problems in -nlcom-. I guess you should fix your fitted model, and figure out why consistency is omitted. Do you really need this triple interaction? Has the previous literature estimated such triple interactions? Etc.

[louisa linkemeyer]

Consistency gets omitted because of collinearity, its a time invariant variable in a fixed-effects model. We have addressed this problem but we were told that the model is still appropiate because we're investigating the moderating effect of consistency and not the effect of consistency on ROA itself.

Do you know if there is any recommended (statistical) literature on the analysis of turning point shift in a moderated u-shaped/curvelinear relationship? The structure of the code with the interactions was used by colleagues of us and they got appropriate results.

[Hong Il Yoo]

louisa linkemeyer: What value do you get when you -display- your expression rather than -nlcom-? If the value is very close to zero, it often helps to scale up the expression initially (see step 1 below, where I multiply your original expression by 1e+10 and apply -nlcom, post-) and then subsequently re-scale it back to original units (see step 2). If 1e+10 doesn't work, try to play around with alternative multiples, e.g., 1e+15, 1e+5, 1e+20 and the like.

 nlcom (step1: 1e+10 * ((_b[csr_score]*_b[c.csr_score#c.csr_score#c.consistency] - _b[c.csr_score#c.csr_score]*_b[c.csr_score#c.co > nsistency]) / 
2*(_b[c.csr_score#c.csr_score]+_b[c.csr_score#c.csr_score#c.consistency]*(-5.954534))^2)), post

nlcom (step2: _b[step1]/1e+10)

Similarly, if the value you get from -display- is very large in magnitude, it often helps to scale down the expression: In the context of the example above, simply replace 1e+10 with 1e-10 in each step.

[Joseph Coveney]

We got the error "Maximum number of iterations exceeded." What can be the reasons for this error? Maybe because consistency got omitted in the regression? Or maybe because of our very low coefficients?

I'd suspect the latter, especially their standard errors.

How can we solve this problem?

Thank you for every little hint

Try dividing your CSR scores by a thousand, or ten thousand or even one-hundred thousand before fitting the model.

-nlcom- needs to use numerical derivatives and first finds the optimum step size iteratively; hence, an -iterate()- option. Your three-way interaction term (especially) and your two-way interaction term are small, and both have practically infinitesimal standard errors to begin with. My guess is that -nlcom- cannot find the optimum (unattainable precision) and runs through the iterations in futility.

[Joseph Coveney]

I hadn't seen Hong's suggestion when I posted mine. I recommend going with his.

version 17.0

clear *

// seedem
set seed 238268142

quietly set obs 250
generate int pid = _n
generate double pid_u = rnormal()
generate double trt = runiform()

quietly expand 10
bysort pid: generate double tim = _n - 5.5

generate double out = tim * tim * trt + pid_u + rnormal()

*
* Begin here
*
summarize trt, meanonly
tempname min
scalar define `min' = r(min)

xtreg out c.tim##c.tim##c.trt, i(pid) fe

capture noisily nlcom ///
    (_b[tim]*_b[tim#tim#trt] - _b[tim#tim] * _b[tim#trt]) / 2 * ///
    (_b[tim#tim] + _b[tim#tim#trt] * `min')^2

display in smcl as text (_b[tim]*_b[tim#tim#trt] - _b[tim#tim] * _b[tim#trt]) / 2 * ///
    (_b[tim#tim] + _b[tim#tim#trt] * `min')^2

nlcom 1e8 * ///
    (_b[tim]*_b[tim#tim#trt] - _b[tim#tim] * _b[tim#trt]) / 2 * ///
    (_b[tim#tim] + _b[tim#tim#trt] * `min')^2

exit

[louisa linkemeyer]

Thank you so much Joseph Coveney & Hong Il Yoo , I decided the CSR Score by 100 and its turned out that this does a really good job for both the coefficient of our regression model and the nlcom code
I really appreciate your help.