___ ____ ____ ____ ____ (R) /__ / ____/ / ____/ ___/ / /___/ / /___/ 16.0 Copyright 1985-2019 StataCorp LLC Statistics/Data Analysis StataCorp 4905 Lakeway Drive Special Edition College Station, Texas 77845 USA 800-STATA-PC http://www.stata.com 979-696-4600 stata@stata.com 979-696-4601 (fax) 10-user Stata network perpetual license: Serial number: 1 Licensed to: Stata Developer StataCorp LLC Notes: 1. Stata is running in batch mode. 2. Unicode is supported; see help unicode_advice. 3. Maximum number of variables is set to 5000; see help set_maxvar. running /home/krg/bin/profile.do ... Compile number 785 . do ratkow3.do . /* NIST/ITL StRD > Dataset Name: Ratkowsky3 (Ratkowsky3.dat) > > File Format: ASCII > Starting Values (lines 41 to 44) > Certified Values (lines 41 to 49) > Data (lines 61 to 75) > > Procedure: Nonlinear Least Squares Regression > > Description: This model and data are an example of fitting > sigmoidal growth curves taken from Ratkowsky (1983). > The response variable is the dry weight of onion bulbs > and tops, and the predictor variable is growing time. > > > Reference: Ratkowsky, D.A. (1983). > Nonlinear Regression Modeling. > New York, NY: Marcel Dekker, pp. 62 and 88. > > > > > > Data: 1 Response (y = onion bulb dry weight) > 1 Predictor (x = growing time) > 15 Observations > Higher Level of Difficulty > Observed Data > > Model: Exponential Class > 4 Parameters (b1 to b4) > > y = b1 / ((1+exp[b2-b3*x])**(1/b4)) + e > > > > Starting Values Certified Values > > Start 1 Start 2 Parameter Standard Deviation > b1 = 100 700 6.9964151270E+02 1.6302297817E+01 > b2 = 10 5 5.2771253025E+00 2.0828735829E+00 > b3 = 1 0.75 7.5962938329E-01 1.9566123451E-01 > b4 = 1 1.3 1.2792483859E+00 6.8761936385E-01 > > Residual Sum of Squares: 8.7864049080E+03 > Residual Standard Deviation: 2.8262414662E+01 > Degrees of Freedom: 9 *** should be 11 *** > Number of Observations: 15 > */ . . clear . program drop _all . . scalar N = 15 . scalar df_r = 11 . scalar df_m = 4 . . scalar rss = 8.7864049080E+03 . scalar rmse = 2.8262414662E+01 . . scalar b1 = 6.9964151270E+02 . scalar seb1 = 1.6302297817E+01 . scalar b2 = 5.2771253025E+00 . scalar seb2 = 2.0828735829E+00 . scalar b3 = 7.5962938329E-01 . scalar seb3 = 1.9566123451E-01 . scalar b4 = 1.2792483859E+00 . scalar seb4 = 6.8761936385E-01 . . qui input double(y x) . . /* The following starting values led to convergence problems: > > nl ( y = {b1} / ( ( 1 + exp( {b2} - {b3}*x ) )^(1/{b4})) ), /// > init(b1 100 b2 10 b3 1 b4 1) > > */ . . nl ( y = {b1} / ( ( 1 + exp( {b2} - {b3}*x ) )^(1/{b4})) ), /// > init(b1 700 b2 5 b3 0.75 b4 1.3) eps(1e-10) (obs = 15) Iteration 0: residual SS = 8838.785 Iteration 1: residual SS = 8788.805 Iteration 2: residual SS = 8786.424 Iteration 3: residual SS = 8786.406 Iteration 4: residual SS = 8786.405 Iteration 5: residual SS = 8786.405 Iteration 6: residual SS = 8786.405 Iteration 7: residual SS = 8786.405 Iteration 8: residual SS = 8786.405 Iteration 9: residual SS = 8786.405 Iteration 10: residual SS = 8786.405 Source | SS df MS -------------+---------------------------------- Number of obs = 15 Model | 3755359.3 4 938839.82 R-squared = 0.9977 Residual | 8786.4049 11 798.764083 Adj R-squared = 0.9968 -------------+---------------------------------- Root MSE = 28.26241 Total | 3764145.7 15 250943.046 Res. dev. = 138.1618 ------------------------------------------------------------------------------ y | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- /b1 | 699.6415 16.3023 42.92 0.000 663.7604 735.5226 /b2 | 5.277129 2.082889 2.53 0.028 .6927216 9.861536 /b3 | .7596297 .1956631 3.88 0.003 .3289782 1.190281 /b4 | 1.27925 .6876225 1.86 0.090 -.2341974 2.792697 ------------------------------------------------------------------------------ . . assert N == e(N) . assert df_r == e(df_r) . assert df_m == e(df_m) . . lrecomp [b1]_b[_cons] b1 [b2]_b[_cons] b2 [b3]_b[_cons] b3 [b4]_b[_cons] b4 ( > ) /* > */ [b1]_se[_cons] seb1 [b2]_se[_cons] seb2 [b3]_se[_cons] seb3 [b4]_se[_cons] > seb4 () /* > */ e(rmse) rmse e(rss) rss [b1]_b[_cons] 7.8 [b2]_b[_cons] 6.2 [b3]_b[_cons] 6.4 [b4]_b[_cons] 6.0 ------------------------- min 6.0 [b1]_se[_cons] 6.4 [b2]_se[_cons] 5.1 [b3]_se[_cons] 5.0 [b4]_se[_cons] 5.3 ------------------------- min 5.0 e(rmse) 11.0 e(rss) 11.4 . . end of do-file