For example, I have a sample loss given default dataset with 317 observations: lgd(real loss given default) is the dependent variable; lgd_a(mean default rate by industry), lev(leverage coefficient by firm) and i_def( mean default rate by year) are independent variables. The kernel distribution is plotted and difficult to be estimated by naked eyes.
data lgddata;
informat lgd lev 12.9 lgd_a 6.4 i_def 4.3;
input lgd lev lgd_a i_def;
label lgd = 'Real loss given default'
lev = 'Leverage coefficient by firm'
lgd_a = 'Mean default rate by year'
i_def = 'Mean default rate by industry';
cards;
0.747573451 0.413989786 0.6261 1.415
/* Other data*/
0.748255544 0.607452819 0.3645 3.783
;
run;
proc kde data = lgddata;
univar lgd / plots = all;
run;
data _lgddata01;
set lgddata;
id + 1;
run;
proc transpose data = _lgddata01 out = _lgddata02 ;
by id;
run;
proc sgplot data = _lgddata02;
hbox col1 / category = _LABEL_;
xaxis label = ' ';
run;
ods html style = money;
%macro modselect(data = , depvar = , kmin= , kmax = , modlist = );
%let modcnt=%eval(%sysfunc(count(%cmpres(&modlist),%str( )))+1);
%do i = 1 %to &modcnt;
%let modelnow = %scan(&modlist, &i);
ods output fitstatistics = &modelnow(rename=(value=&modelnow));
ods select densityplot fitstatistics;
proc fmm data = &data;
model &depvar = / kmin=&kmin kmax= &kmax dist=&modelnow;
run;
%end;
data _final;
%do i = 1 %to &modcnt;
set %scan(&modlist, &i);
%end;
run;
proc sgplot data = _tmp01;
%do i = 1 %to &modcnt;
%let modelnow = %scan(&modlist, &i);
series x = descr y = &modelnow;
where descr ne :'E' and descr ne :'P';
%end;
yaxis label = ' ' grid;
run;
proc transpose data = _tmp01 out = _tmp02;
where descr = :'E' or descr = :'P';
id descr;
run;
proc sgplot data = _tmp02;
bubble x = effective_parameters y = effective_components
size = pearson_statistic / datalabel = _name_;
xaxis grid; yaxis grid;
run;
%mend;
%modselect(data = lgddata, depvar = lgd, kmin= 1,
kmax = 10, modlist = beta lognormal gamma);
Then I chose the 5-compenent Homogeneous beta distribution to model the LGD data. PROC FMM provided all parameter estimates for these 5 components. From the plot above, the intercepts and the scale parameter s are different as expected. Interestingly, the parameters of lgd_a(mean default rate by industry) present big diversity, while the parameters of i_def( mean default rate by year) tend to converge at the zero point.
ods output parameterestimates = parmds;
proc fmm data = lgddata;
model lgd = lev lgd_a i_def / k = 5 dist=beta;
run;
proc sgplot data = parmds;
series x = Effect y = Estimate / group = Component;
xaxis grid label = ' '; yaxis grid;
run;
ods html style = htmlbluecml;
