r.rational.regression(1)Grass User's Manualr.rational.regression(1)



NNAAMMEE
       rr..rraattiioonnaall..rreeggrreessssiioonn  -  linear  and nonlinear regression
       calculation from data stored in ASCII file

       _(_G_R_A_S_S _R_a_s_t_e_r _P_r_o_c_e_s_s_i_n_g _P_r_o_g_r_a_m_)

SSYYNNOOPPSSIISS
       rr..rraattiioonnaall..rreeggrreessssiioonn

       rr..rraattiioonnaall..rreeggrreessssiioonn hheellpp

       rr..rraattiioonnaall..rreeggrreessssiioonn	    iinnppuutt==_n_a_m_e	      oouuttppuutt==_n_a_m_e
       [cchheecckk==_"_p_h_r_a_s_e_"]  [pprreeddiicctt==_"_p_h_r_a_s_e_"] [pplloott==_"_p_h_r_a_s_e_"] [ccaall--
       ccuullaatt==_"_p_h_r_a_s_e_"]

DDEESSCCRRIIPPTTIIOONN
       The _r_._r_a_t_i_o_n_a_l_._r_e_g_r_e_s_s_i_o_n program calculates the linear or
       nonlinear  regression  model.   If  it is used as an image
       precessing tool, the multispectral  space  remote  sensing
       data will be the regression variables (ascii file) and the
       ground  vegetation  coverage  measurements  will  be   the
       response variables (also ascii file) and this command will
       be useful for obtaining	linear	or  nonlinear  regression
       models from the remote-sensing data which have correspond-
       ing ground mearsurement and for predicting vegetation cov-
       erage using other remote-sensing data which have no corre-
       sponding ground truth records.  The  input  file  has  the
       following format


       regression valuables x1, x2, ... response variable y


       channel 1 (x1)	channel 2 (x2) ...  coverage


       For  a  three channel remote-sensing data the following is
       an example of input ascii file

       0.4350	 0.2616      0.7016	   0.98

       0.4140	 0.2620      0.6520	   0.99

       0.4940	 0.3500      0.5580	   0.34

       0.5983	 0.5350      0.5650	   0.10

       0.4883	 0.3733      0.5533	   0.88

       0.4150	 0.2916      0.5116	   0.60

       0.5566	 0.5250      0.5466	   0.09

       0.4420	 0.2820      0.6800	   0.86

       0.4220	 0.2620      0.6260	   0.88

       0.4766	 0.3666      0.5933	   0.61

       0.5180	 0.4300      0.5140	   0.60

       0.4416	 0.2700      0.7383	   0.96

       0.4583	 0.3116      0.5133	   0.76

       0.4300	 0.2750      0.7233	   0.98

       0.4320	 0.2760      0.6460	   1.00

       0.4733	 0.3566      0.5616	   0.53

       0.4200	 0.2450      0.7966	   1.00

       0.4850	 0.3533      0.7216	   0.99

       0.4360	 0.2620      0.7620	   0.99

       0.4283	 0.2650      0.6783	   0.91

       0.4633	 0.3200      0.6750	   0.94


       The resulted regression model  (coefficient  numbers)  and
       related	information about the confidencial test, goodness
       or utility test (e.g., correlation coefficient  r  between
       observed and calculated coverage, F value and t value) are
       put on the output file (ascii file also).


       Eight models can be choosen by user after prompted by  the
       program.  They are:


       1)      usual	  linear      model:	 y=a[0]x[0]+a[1],
       y=a[0]x[0]+a[1]x[1]+a[2] y=a[0]x[0]+a[1]x[1]+a[2]x[2]+a[4]


       2) linear model with remote-sensing data normalized by the
       data in	the  first  spectrial  band;  normalized  by  x1:
       y=a[0]x[1]/x[0]	+  a[1] y=a[0]x[1]/x[0] + a[1]x[2]/x[0] +
       a[2]


       3) linear model with normalization  by  the  second  band;
       normalized by x2: y=a[0]x[0]/x[1] + a[1] y=a[0]x[0]/x[1] +
       a[1]x[2]/x[1] + a[2]


       4) NDVI (normalized differential vegetation index) model;


       5) NDVI model for intensity instead of radiance;


       6) NDVI model for reflectance;


       7) semi-relaxation vegetation index model;


       8) RVI (relaxation vegetation index) nonlinear model.


       The user has three options for check: multx1, multx2,  and
       multx3.	 These	options  check	multi-collinearity of the
       input data. multx1 calculates $R sup  2$  for  channel  x1
       being  replaced	by  coverage  y. multx2 for channel x2 if
       input data are composed of  two	remote-sensing	channels.
       And multx3 for channel x3 if input data are composed of at
       least three channels.


       The program provides three methods to conduct the  nonlin-
       ear  regression calculation.  These methods can be invoked
       by the user as options of  calculat.   The  first  one  is
       rational fraction method.  If no any option of calculat is
       given by the  user,  the  program  will	adopt  the  first
       method.	If calculat = rvi_linear the linearization method
       is taken to conduct the nonlinear relaxation index regres-
       sion.   If  the user set calculat = rvi_nonlinear the gen-
       eral nonlinear regression method is used.  If  calculat	=
       all,   the program will conduct nonlinear regression first
       using the rational fraction  method  and  then  using  the
       obtained  coefficients  as  initial  values to conduct the
       second method calculation  and  finally	using  the  third
       method  to  improve  the results. For nonlinear regression
       calculation there may exist multi-minimums.  We can not be
       in  reliance  on  the  existing usual algorithms which can
       find one minimum only.  The computer  will  not	scan  the
       possible  minimums  in  order to save  computer time.  The
       user should judge and select a least  minimum  during  the
       iteration.  The necessary parameters which will facilitate
       the judgement for each  iteration  are  displayed  in  the
       screen and also output to the output file.


       For  plots of relavant features of the regression calcula-
       tion the user can set option for  plot.	 There	are  four
       options	for  the  plot.  If plot = radiance-coverage com-
       puter will send radiance data against  coverage	data  for
       further	plotting  radiance-coverage  curves or figures to
       show the scatter of input data.	This data will stored  in
       ascii	 files	  named    "curve.radiance_coverage_x1y",
       "curve.radiance_coverage_x2y"  and  "curve.radiance_cover-
       age_x3y".   If  plot  =	vegetation-soil  three ascii data
       files  will  be	generated  by  the  program  for  further
       figuers.    Their   names   are	 "curve.veget_soil_x1x2",
       "curve.veget_soil_x1x3" and  "curve.veget_soil_x2x3".   If
       the  user  set  plot  = adequacy the program will generate
       residual data files  for  plotting  figures  of	residuals
       against predictors and dependent variable to show the ade-
       quacy. These files named curve_residual_x1", "curve_resid-
       ual_x2",  "curve_residual_x3"  and "curve_residual_y".  If
       plot = all the program will generate all these above  men-
       tioned  data  files for further plotting of different fig-
       ures.


       The program not only can calculate regression  models  but
       also  can make prediction to new remote sensing data using
       the obtained model.  The user can set option of predict	=
       same  to  calculate  regression	model  using  part of one
       imagery data and predict vegetation coverage  for  another
       part  of remote sensing data in the same imagery.  If pre-
       dict = other the program  will  use  one  imagery  to  get
       regression model and predict vegetation coverage for other
       imagery.  If the user did not give any option for  predict
       the program calculates model based on the whole input data
       and not conduct any prediction.	The program still  gener-
       ate  a  set  of "calculated vegetation coverage" using the
       obtained model and the same input data in  order  for  the
       user  to check the utility, goodness and confidencial sta-
       tus of the regression. _r_._r_a_t_i_o_n_a_l_._r_e_g_r_e_s_s_i_o_n will  be  run
       non-interactively  if the user specifies program arguments
       on the command line, using the form:


       _r_._r_a_t_i_o_n_a_l_._r_e_g_r_e_s_s_i_o_n	    _i_n_p_u_t_=_n_a_m_e	      _o_u_t_p_u_t_=_n_a_m_e
       _[_c_h_e_c_k_=_"_p_h_r_a_s_e_"_]  _[_p_r_e_d_i_c_t_=_"_p_h_r_a_s_e_"_] _[_p_l_o_t_=_"_p_h_r_a_s_e_"_] _[_c_a_l_-
       _c_u_l_a_t_=_"_p_h_r_a_s_e_"_]


       But after run, the computer will prompt the user to select
       model number.

       Alternately, the user can simply type:


       _r_._r_a_t_i_o_n_a_l_._r_e_g_r_e_s_s_i_o_n


       on  the	command  line without program arguments.  In this
       case, the user will be prompted for parameter values using
       the  standard GRASS user interface described in the manual
       entry for _p_a_r_s_e_r.

OOPPTTIIOONNSS
   PPaarraammeetteerrss::
       cchheecckk== For check of multi-collinearity.	Options:  multx1,
	      multx2, multx3

       ccaallccuullaatt==
	      Method  of  calculation  for  nonlinear regression.
	      Options: rvi_linear, rvi_nonlinear, all

       pplloott==  Name of data files generated  by	the  program  for
	      further plotting.  Options: radiance-coverage, veg-
	      etation-soil, adequacy, all

       pprreeddiicctt==
	      Fashion of prediction.  Options: same, other


SSEEEE AALLSSOO
       _i_._n_d_v_i_, _r_._l_i_n_e_a_r_._r_e_g_r_e_s_s_i_o_n


AAUUTTHHOORRSS
       Hong  C.  Zhuang,  U.S.	Army   Construction   Engineering
       Research  Laboratory  Department  of  Electrical  Computer
       Engeering, University of Illinois at Urbana-Champiagn.


       Michael	Shapiro,  U.S.	Army   Construction   Engineering
       Research Laboratory.

       _L_a_s_t _c_h_a_n_g_e_d_: _$_D_a_t_e_: _2_0_0_2_/_0_1_/_2_5 _0_5_:_4_5_:_3_4 _$



GRASS 5.0				 r.rational.regression(1)
