Oleh Komashko 0.38 2026-07-17 obtains weights to use in wls, GQ het. test C20 C12 Goldfeld - Quandt test MODELWIN/Tests The package contains 2 functions to obtain weights to use in wls for popular versions of feasible weighted least squares. In addition it performs Goldfeld - Quandt heteroskedasticity test. It includes 5 public functions. Test: gqtest(), GUI_gqtest(), gqtest_print(). Wls-helpers: clustweights(), expweights() The main reason for this package is pedagogical. There are plethora of books "Using Soft (e.g., Stata, Eviews, Excel) with Hill Griffiths Lim". And there exists a possibility of someone making an opinion of a piece of software by comparing how simple is to solve computer exercises in it. The package contains two functions to compute clustered and exponential weights for further use with wls. Additionally, the package allows testing group-wise heteroskedasticity as in HGL, 4-th, 8.2.3. As Prof. Riccardo Lucchetti wrote: "Nobody uses this test anymore in serious empirical research, and it's rapidly disappearing from textbooks as well." But the package author thinks it can be useful for the courses relying upon HGL. FUNCTIONS DESCRIPTION function matrix gqtest (series y "the dependent var", list xl "independent vars, include 'const', if required", series sby[null] "variable to sort by", scalar c[0:1:NA]) "fraction of middle obs. to omit") Outputs a 1 by 4 matrix: F-statistics, 2 degrees of freedom, and 2-sided p-value. Always prints the results. This function doesn't support panel data. Parameters: c - must be in (0,1), for the only exception see below, fraction of the sample to omit; default is 1/3 sby - variable to sort observations by if 'sby' is dummy, 'c' is ignored, the sample split rule is 0/1 if 'sby' is integer variable with 3 distinct values, and c=1 sby is used for idiosyncratic splitting of the sample with observations, corresponding to the middle value omitted. if 'sby' = 'const', observations are not sorted, as in time series setting. if sby is missed, it is set as 'const' Usage: nulldata 24 series y = normal(0,1) x1 = normal(0,1) x2 = normal(0,1) series qwerty = normal(0,1) list xl = 0 x1 x2 d = (obs>14) dd = (obs<6)+2*(obs>16) gqtest(y,xl) # data sorted by y; middle 1/3 omitted gqtest(y,xl,qwerty) # data sorted by qwerty; middle 1/3 omitted gqtest(y,xl,const) # data unsorted ; middle 1/3 omitted gqtest(y,xl,d) # 'c' ignored gqtest(y,xl,dd,1) # obs. with middle values of dd omitted function bundle GUI_gqtest (series sby[null] "variable to sort by", scalar c[NA] "fraction of middle obs. to omit") GUI path: model window (ols)-> tests The GUI version omits 2 first arguments in comparison with script version, since the dependent variable and regressors are the same as in the estimated model. function void gqtest_print (bundle *b) A helper to GUI version: the script version outputs a matrix and prints the results by default. This function doesn't support panel data. function series clustweights (series y "the dependent variable", list xlist "independent variables", series clustvar "cluster variable") Computes weights series to use in wls estimation for grouped data, as described in POE-4, s. 8.4.2. Example (datafile from POE-4): open cps2.gdt list xlist = 0 educ exper metro w = clustweights (wage, xlist, metro) wls w wage xlist function series expweights (series y "the dependent variable", list xlist "independent variables", list zlist[null] "sd vars, null: logs xlist, zlist=xlist==hsk") Computes weights series to use in wls estimation according to the following model for variance: log(sigma_i^2) = const + z'_i*alpha See, e.g POE-4, s. 8.5. zlist = null means zlist = log(xlist), if possible Example (datafile from POE-4): variables in the variance model are the logarithms of the original regression variables open food.gdt list xlist = 0 income series wtb = expweights(food_exp, xlist) wls wtb food_exp 0 income List of abbreviations POE - gretl data set to Principles of Econometrics. HGL, POE-4 - Hill, Griffiths, Lim - Principles of Econometrics - Fourth Edition. NEWS in 0.3 Printing pvalues for one-sided alternatives added to qgtest 2 new functions added: clustweights(), expweights(). NEWS in 0.38 Type of sby in qtest() changed to series. Some changes in help file. the dependent variable independent variables cluster variable cvals = uniq(clustvar) ncv = nelem(cvals) matrix sigmas = zeros(ncv,1) loop i=1..ncv -q smpl (clustvar==cvals[i]) --restrict --replace ols y xlist -q sigmas[i] = $sigma endloop smpl full series www = 0 loop i=1..ncv -q www = www+(clustvar==cvals[i])/(sigmas[i])^2 endloop www = www/sd(www) setinfo www --description="cluster weights" return www variable to sort by fraction of middle obs. to omit bundle b list Y = $ylist string yname = $depvar loop foreach i Y -q series @yname = Y.$i endloop list xlist = $xlist if missing(c) c=1/3 endif aaaaa = exists(sby) #print aaaaa if aaaaa == 0 #series sby = @yname #sby = const bundle b = gqtest_gui(@yname,xlist,const,c) else uaa = uniq(sby) tuaa = typeof(uaa) if tuaa == 1 && uaa == 1 bundle b = gqtest_gui(@yname,xlist,const,c) else bundle b = gqtest_gui(@yname,xlist,sby,c) endif endif #list sby = bys #if nelem(sby)==0 # sby = const #endif #print sby #bundle b = gqtest_gui(@yname,xlist,sby,c) return b matrix ret = b["ret"] scalar F = ret[1] scalar df1 = ret[2] scalar df2 = ret[3] scalar pv = ret[4] scalar pvg = ret[5] scalar pvl = ret[6] scalar check1 = b["check1"] scalar check2 = b["check2"] scalar t1 = b["t1"] scalar t2 = b["t2"] string ay = b["ay"] string sss = b["sss"] printf "\nGoldfeld - Quandt heteroskedasticity test.\n\n" if check1 printf "%d first valid observations (s1^2)\n", t1 printf "and %d last valid observations were used (s2^2).\n", t2 else if check2 printf "%d observations with %s = 0 (s1^2)\n", t1, ay printf "and %d with %s = 1 were used (s2^2).\n", t2, ay else printf "%d observations with the smallest value%s (s1^2)\n", t1, sss printf "and %d with the largest value%s of '%s' were used (s2^2).\n", t2, sss, ay endif endif printf "\nTest statistic: s2^2/s1^2 = F(%d,%d) = %.6g\n", df2, df1, F printf "H1(s1^2 != s2^2): pvalue = %.4f\n", pv printf "H1(s1^2 < s2^2): pvalue = %.4f\n", pvg printf "H1(s1^2 > s2^2): pvalue = %.4f\n\n", pvl the dependent variable independent variables variance model vars; null: log(xlist) if nelem(zlist)==0 list x0 = xlist-0 l_x0 = log(x0) zlist = const l_x0 else if !(inlist(zlist,const)) zlist = const zlist endif endif ols y xlist -q series lnsighat = ln($uhat^2) ols lnsighat zlist -q matrix alpha = $coeff series wt = 1/exp(lincomb(zlist, alpha)) wt = wt/sd(wt) setinfo wt --description="exp. weights" return wt the dependent var independent vars, include 'const', if required variable to sort by fraction of middle obs. to omit # this function doesn't support panel data if missing(c) c=1/3 endif if (c<=0)||(c>1) funcerr "Wrong fraction value" endif if $datatype == 3 funcerr "this function dosn't support panel data" endif #print missing(sby) #if is_null(sby) #series sby = const #endif #aaaaa = exists(argname(sby)) aaaaa = exists(sby) #print aaaaa if aaaaa == 0 series sby = const endif uaa = uniq(sby) #eval argname(sby) list lysby = sby nsby = nelem(lysby) list xxxl = y xl if nsby>1 funcerr "Only one variable can be included as the third argument" elif nsby==1 series z = lysby[1] #series z = sby list xxxl = y xl uuu = inlist(xxxl,lysby[1]) if uuu>0 smpl xxxl --no-missing else xxxl = xxxl sby smpl xxxl --no-missing endif #ay = varname(sby) tuaa = typeof(uaa) #suaa = "tuaa" #print suaa tuaa #ay = uaa == const #print ay #ay = "foo" if tuaa == 1 && uaa == 1 ay = "const" else ay = argname(sby) endif #print ay if c==1 val = values(lysby[1]) rval = round(val) ddd = (val.=rval) nval = nelem(val) sval = sum(ddd) if (nval==3)&&(sval==3) d1=(lysby[1]==val[1]) d2=(lysby[1]==val[3]) smpl d1==1 --restrict else funcerr "Wrong fraction value" endif else if ay == "const" T = $nobs n1 = round(T*(1-c)/2) smpl 1 n1 elif isdummy(lysby[1]) smpl lysby[1]==0 --restrict else scalar cutpoint_lo = quantile(lysby[1], c) scalar cutpoint_hi = quantile(lysby[1], (1-c)) smpl lysby[1]<=cutpoint_lo --restrict endif endif else if c==1 funcerr "Wrong fraction value" endif smpl y xl --no-missing scalar cutpoint_lo = quantile(y, c) scalar cutpoint_hi = quantile(y, (1-c)) smpl y<=cutpoint_lo --restrict ay = argname(y) endif ols y xl --quiet scalar df1 = $df scalar den = $ess / df1 scalar t1 = $T smpl full smpl xxxl --no-missing if nsby==1 if c==1 smpl d2==1 --restrict else if ay == "const" T = $nobs n2 = T-n1+1 smpl obs>=n2 --restrict elif isdummy(lysby[1]) smpl lysby[1]==1 --restrict else smpl lysby[1]>=cutpoint_hi --restrict endif endif else smpl y>=cutpoint_hi --restrict endif ols y xl --quiet scalar df2 = $df scalar num = $ess / df2 scalar t2 = $T scalar F = num/den ff = den/num print ff scalar pv = pvalue(F,df2,df1,F) scalar pvg = pv scalar pvl = 1 - pv pv = 2*xmin(pv,(1-pv)) smpl full if c==1 sss ="" else sss="s" endif printf "\nGoldfeld - Quandt heteroskedasticity test.\n\n" if ay == "const" printf "%d first valid observations (s1^2)\n", t1 printf "and %d last valid observations were used (s2^2).\n", t2 else if (nsby==1)&&(isdummy(lysby[1])) printf "%d observations with %s = 0 (s1^2)\n", t1, ay printf "and %d with %s = 1 were used (s2^2).\n", t2, ay else printf "%d observations with the smallest value%s (s1^2)\n", t1, sss printf "and %d with the largest value%s of '%s' were used (s2^2).\n", t2, sss, ay endif endif printf "\nTest statistic: s2^2/s1^2 = F(%d,%d) = %.6g\n", df2, df1, F printf "H1(s1^2 != s2^2): pvalue = %.4f\n", pv printf "H1(s1^2 < s2^2): pvalue = %.4f\n", pvg printf "H1(s1^2 > s2^2): pvalue = %.4f\n\n", pvl ret = F~df1~df2~pv~pvg~pvl return ret scalar err = 0 string cmd = $command if cmd != "ols" print "gqtest: not an ols model" err = 1 endif return err the dependent var independent vars, include 'const', if required variable to sort by fraction of middle obs. to omit set echo off set messages off if missing(c) c=1/3 endif if (c<=0)||(c>1) funcerr "Wrong fraction value" endif nsby = nelem(sby) list xxxl = y xl if nsby>1 funcerr "Only one variable can be included as the third argument" elif nsby==1 series z = sby[1] list xxxl = y xl uuu = inlist(xxxl,sby[1]) if uuu>0 smpl xxxl --no-missing else xxxl = xxxl sby smpl xxxl --no-missing endif ay = varname(sby) if c==1 val = values(sby[1]) rval = round(val) ddd = (val.=rval) nval = nelem(val) sval = sum(ddd) if (nval==3)&&(sval==3) d1=(sby[1]==val[1]) d2=(sby[1]==val[3]) smpl d1==1 --restrict else funcerr "Wrong fraction value" endif else if ay == "const" T = $nobs n1 = round(T*(1-c)/2) smpl 1 n1 elif isdummy(sby[1]) smpl sby[1]==0 --restrict else scalar cutpoint_lo = quantile(sby[1], c) scalar cutpoint_hi = quantile(sby[1], (1-c)) smpl sby[1]<=cutpoint_lo --restrict endif endif else if c==1 funcerr "Wrong fraction value" endif smpl y xl --no-missing scalar cutpoint_lo = quantile(y, c) scalar cutpoint_hi = quantile(y, (1-c)) smpl y<=cutpoint_lo --restrict ay = argname(y) endif m1 <- ols y xl --quiet scalar df1 = m1.$df scalar den = m1.$ess / df1 scalar t1 = m1.$T smpl full smpl xxxl --no-missing if nsby==1 if c==1 smpl d2==1 --restrict else if ay == "const" T = $nobs n2 = T-n1+1 smpl obs>=n2 --restrict elif isdummy(sby[1]) smpl sby[1]==1 --restrict else smpl sby[1]>=cutpoint_hi --restrict endif endif else smpl y>=cutpoint_hi --restrict endif m2 <- ols y xl --quiet scalar df2 = m2.$df scalar num = m2.$ess / df2 scalar t2 = m2.$T scalar F = num/den scalar pv= pvalue(F,df2,df1,F) scalar pvg = pv scalar pvl = 1 - pv pv = 2*xmin(pv,(1-pv)) smpl full if c==1 sss ="" else sss="s" endif bundle b check1 = (ay == "const") print check1 check2 = (nsby==1)&&(isdummy(sby[1])) print check2 ret = F~df1~df2~pv~pvg~pvl b["ret"] = ret b["check1"] = check1 b["check2"]=check2 b["t1"] = t1 b["t2"] = t2 b["ay"] = ay b["sss"] = sss return b # sample function call include gqtest.gfn ###### The test ### different usages set messages off set echo off nulldata 24 # for reproducibility set seed 147 series y = normal(0,1) x1 = normal(0,1) x2 = normal(0,1) series qwerty = normal(0,1) list xl = 0 x1 x2 # dummy d = (obs>14) # integer variable with 3 distinct values dd = (obs<6)+2*(obs>16) set echo on gqtest(y,xl) # data sorted by y; middle 1/3 omitted gqtest(y,xl,qwerty) # data sorted by qwerty; middle 1/3 omitted gqtest(y,xl,const) # data unsorted ; middle 1/3 omitted gqtest(y,xl,d) # 'c' ignored gqtest(y,xl,dd,1) # obs. with middle values of dd omitted ###### wls-helpers open data7-2 list xlist = 0 EDUC EXPER AGE GENDER w = clustweights (WAGE, xlist,GENDER) wls w WAGE xlist w1 = expweights(WAGE, xlist) wls w1 WAGE xlist w2 = expweights(WAGE, xlist, xlist) wls w2 WAGE xlist # the same hsk WAGE xlist --no-squares --quiet eval $coeff