Dear Statalisters,
After a couple of failed attempts I am again seeking a help regarding Confidence interval of a quotient by Fieller's method. I tried to replicate the community-contributed module, however the nature of the example from the attached link (http://fmwww.bc.edu/RePEc/bocode/f/fieller.html) is completely different. Therefore I failed to reproduce a meaningful/logical results. To be more precise, I would like to display my dataset and the way a treat the data in order to find our the Confidence interval of a quotient by Fieller's method.
I use a credit risk as a dependent variable and the direct (adjusted lerner) and the squared term (of adjusted lerner) as explanatory variables. I managed to find the turning point by running a random-effects negative binomial model (supported by a Hausman test - xtnberg). Please see below my results:
Followed by
And the results are the following:
In my case I suppose that blood pressure (bp) should be replicated with credit risk, however I am not quite sure what is the logic of
.
I tried to replicate the command by using my own logic and got the following results:
However, this doesn't make sense from my point of view. As far as I know the result for extreme point should be between the result of 0.00944809–0.20789796 (in my case). Could you please advise how should I treat this type of test taking into account my data? Perhaps I am using the wrong dependent variable, or the whole logic is wrong?
On the other hand, I also tried to An alternative approach (for large samples) using the delta method;
The command used based on my data and according to the attached link is the follows:
Again the results do not make sense as the Conf. Interval is negative? Is this normal or again I am doing a wrong test.
Many thanks in advance for your always precious help,
Petko Bachvarov
After a couple of failed attempts I am again seeking a help regarding Confidence interval of a quotient by Fieller's method. I tried to replicate the community-contributed module, however the nature of the example from the attached link (http://fmwww.bc.edu/RePEc/bocode/f/fieller.html) is completely different. Therefore I failed to reproduce a meaningful/logical results. To be more precise, I would like to display my dataset and the way a treat the data in order to find our the Confidence interval of a quotient by Fieller's method.
I use a credit risk as a dependent variable and the direct (adjusted lerner) and the squared term (of adjusted lerner) as explanatory variables. I managed to find the turning point by running a random-effects negative binomial model (supported by a Hausman test - xtnberg). Please see below my results:
Code:
xtnbreg llrgl car adjlerner adjlerner2 insitution ownership_concentration cir deposit_asset loan_asset otherearningassets incomediversity size tier1 fundingragility luqidasset logz gdp_growth inflation crisis_d listed_d, fe
Code:
utest adjlerner adjlerner2, prefix(llrgl)
Code:
Conditional FE negative binomial regression Number of obs = 3124
Group variable: y Number of groups = 14
Obs per group: min = 223
avg = 223.1
max = 225
Wald chi2(19) = 95.47
Log likelihood = -481.71589 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
CreditRisk | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
car | .0480899 .3682911 0.13 0.896 -.6737474 .7699271
adjlerner | -5.870174 1.569279 -3.74 0.000 -8.945904 -2.794444
adjlerner2 | 7.036934 1.943191 3.62 0.000 3.22835 10.84552
insitution | -.1541609 .1247337 -1.24 0.216 -.3986344 .0903125
ownership~on | .0115567 .2493661 0.05 0.963 -.4771918 .5003052
cir | .0020299 .002605 0.78 0.436 -.0030758 .0071356
deposit_as~t | .686342 .4698969 1.46 0.144 -.2346389 1.607323
loan_asset | -2.129252 .5312894 -4.01 0.000 -3.17056 -1.087944
otherearni~s | .216634 .346283 0.63 0.532 -.4620682 .8953361
incomedive~y | .142058 .1615877 0.88 0.379 -.174648 .458764
size | .0747654 .039163 1.91 0.056 -.0019926 .1515234
tier1 | .0816059 .2788698 0.29 0.770 -.464969 .6281807
fundingrag~y | .0959053 .4705931 0.20 0.839 -.8264402 1.018251
luqidasset | .860141 .4811945 1.79 0.074 -.082983 1.803265
logz | .0032852 .0652955 0.05 0.960 -.1246917 .1312621
gdp_growth | -5.295671 1.911873 -2.77 0.006 -9.042874 -1.548468
inflation | -.130405 1.155299 -0.11 0.910 -2.39475 2.13394
crisis_d | .0278075 1.120135 0.02 0.980 -2.167616 2.223231
listed_d | .356337 .1745903 2.04 0.041 .0141463 .6985277
_cons | 13.40707 203.6382 0.07 0.948 -385.7164 412.5306
------------------------------------------------------------------------------
. utest adjlerner adjlerner2, prefix(llrgl)
(325 missing values generated)
Specification: f(x)=x^2
Extreme point: .4170974
Test:
H1: U shape
vs. H0: Monotone or Inverse U shape
-------------------------------------------------
| Lower bound Upper bound
-----------------+-------------------------------
Interval | -.1606019 .9939588
Slope | -8.130464 8.11867
t-value | -3.729346 3.42437
P>|t| | .0000977 .0003121
-------------------------------------------------
Overall test of presence of a U shape:
t-value = 3.42
P>|t| = .000312
.
Code:
bysort when: fieller bp, by(sex) level(90)
Code:
by(sex)
I tried to replicate the command by using my own logic and got the following results:
Code:
. fieller CreditRisk, by(banks) level(95) Confidence Interval for a Quotient by Fieller's Method (Unpaired Data) Numerator Mean: .01406786 Denominator Mean: .25610064 Quotient: .05493098 95% CI: .00944809–.20789796
On the other hand, I also tried to An alternative approach (for large samples) using the delta method;
The command used based on my data and according to the attached link is the follows:
Code:
reg CreditRisk adjlerner adjlerner2, noconstant
Source | SS df MS Number of obs = 3124
-------------+------------------------------ F( 2, 3122) = 430.76
Model | 10.0026565 2 5.00132827 Prob > F = 0.0000
Residual | 36.2479737 3122 .011610498 R-squared = 0.2163
-------------+------------------------------ Adj R-squared = 0.2158
Total | 46.2506302 3124 .014804939 Root MSE = .10775
------------------------------------------------------------------------------
CreditRisk | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
adjlerner | -.1147687 .0198311 -5.79 0.000 -.153652 -.0758855
adjlerner2 | .1708729 .0164604 10.38 0.000 .1385986 .2031473
------------------------------------------------------------------------------
Code:
nlcom _b[adjlerner] / _b[adjlerner2]
------------------------------------------------------------------------------
llrgl | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_nl_1 | -.6716614 .0532586 -12.61 0.000 -.7760869 -.5672359
Many thanks in advance for your always precious help,
Petko Bachvarov
