> salm.mod1 <- nls(resp ~ (b0+exp(b1+b2*log(dose)))*exp(-b3*dose), + start=c(b0=20,b1=10,b2=1,b3=1),weight=varwt,data=expt1) > summary(salm.mod1) Formula: resp ~ (b0 + exp(b1 + b2 * log(dose))) * exp(-b3 * dose) Parameters: Estimate Std. Error t value Pr(>|t|) b0 23.15862 2.93625 7.887 4.43e-07 *** b1 7.21858 0.04328 166.800 < 2e-16 *** b2 1.00008 0.02941 34.001 < 2e-16 *** b3 0.26099 0.02512 10.389 8.82e-09 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 1.174 on 17 degrees of freedom Number of iterations to convergence: 7 Achieved convergence tolerance: 9.246e-07 > deviance(salm.mod1) [1] 23.43436 > > > expt2 <- subset(salmonella,expt==2) > > salm.mod2 <- nls(resp ~ (b0+exp(b1+b2*log(dose)))*exp(-b3*dose), + start=c(b0=20,b1=10,b2=1,b3=1),weight=varwt,data=expt2) > summary(salm.mod2) Formula: resp ~ (b0 + exp(b1 + b2 * log(dose))) * exp(-b3 * dose) Parameters: Estimate Std. Error t value Pr(>|t|) b0 21.19355 2.52609 8.390 1.90e-07 *** b1 7.26329 0.04514 160.891 < 2e-16 *** b2 1.20024 0.05033 23.846 1.66e-14 *** b3 0.30620 0.03571 8.574 1.40e-07 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 0.9569 on 17 degrees of freedom Number of iterations to convergence: 8 Achieved convergence tolerance: 6.668e-07 > deviance(salm.mod2) [1] 15.56472 > > salm.mod3 <- nls(resp ~ (b0+exp(b1+b2*log(dose)))*exp(-b3*dose), + start=c(b0=20,b1=10,b2=1,b3=1),weight=varwt,data=salmonella) > summary(salm.mod3) Formula: resp ~ (b0 + exp(b1 + b2 * log(dose))) * exp(-b3 * dose) Parameters: Estimate Std. Error t value Pr(>|t|) b0 22.47948 2.78895 8.060 9.50e-10 *** b1 7.18192 0.03789 189.527 < 2e-16 *** b2 1.01137 0.03136 32.246 < 2e-16 *** b3 0.24730 0.02474 9.998 3.43e-12 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 1.537 on 38 degrees of freedom Number of iterations to convergence: 7 Achieved convergence tolerance: 7.495e-06 > deviance(salm.mod3) [1] 89.71255 > > salm.mod4 <- nls(resp ~ expt01*(b02+exp(b12+b22*log(dose)))*exp(-b32*dose) + + (1-expt01)*(b01+exp(b11+b21*log(dose)))*exp(-b31*dose), + start=c(b01=20,b11=10,b21=1,b31=1,b02=20,b12=10,b22=1,b32=1), + weight=varwt,data=salmonella) > summary(salm.mod4) Formula: resp ~ expt01 * (b02 + exp(b12 + b22 * log(dose))) * exp(-b32 * dose) + (1 - expt01) * (b01 + exp(b11 + b21 * log(dose))) * exp(-b31 * dose) Parameters: Estimate Std. Error t value Pr(>|t|) b01 23.15862 2.67842 8.646 4.21e-10 *** b11 7.21858 0.03948 182.857 < 2e-16 *** b21 1.00008 0.02683 37.274 < 2e-16 *** b31 0.26099 0.02292 11.389 3.77e-13 *** b02 21.19355 2.82742 7.496 1.06e-08 *** b12 7.26329 0.05053 143.744 < 2e-16 *** b22 1.20024 0.05634 21.305 < 2e-16 *** b32 0.30620 0.03997 7.660 6.64e-09 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 1.071 on 34 degrees of freedom Number of iterations to convergence: 8 Achieved convergence tolerance: 4.08e-07 > deviance(salm.mod4) [1] 38.99907 > > salm.mod5 <- nls(resp ~ expt01*(b02+exp(b1+b22*log(dose)))*exp(-b3*dose) + + (1-expt01)*(b01+exp(b1+b21*log(dose)))*exp(-b3*dose), + start=c(b01=20,b1=10,b21=1,b3=1,b02=20,b22=1), + weight=varwt,data=salmonella) > summary(salm.mod5) Formula: resp ~ expt01 * (b02 + exp(b1 + b22 * log(dose))) * exp(-b3 * dose) + (1 - expt01) * (b01 + exp(b1 + b21 * log(dose))) * exp(-b3 * dose) Parameters: Estimate Std. Error t value Pr(>|t|) b01 23.74539 2.62425 9.048 8.37e-11 *** b1 7.22017 0.02721 265.338 < 2e-16 *** b21 1.00623 0.02239 44.948 < 2e-16 *** b3 0.26541 0.01772 14.978 < 2e-16 *** b02 20.48947 2.75871 7.427 9.11e-09 *** b22 1.14898 0.03170 36.242 < 2e-16 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 1.066 on 36 degrees of freedom Number of iterations to convergence: 7 Achieved convergence tolerance: 2.445e-06 > deviance(salm.mod5) [1] 40.89001 > > salm.mod6 <- nls(resp ~ expt01*(b0+exp(b1+b22*log(dose)))*exp(-b3*dose) + + (1-expt01)*(b0+exp(b1+b21*log(dose)))*exp(-b3*dose), + start=c(b0=20,b1=10,b21=1,b3=1,b22=1), + weight=varwt,data=salmonella) > summary(salm.mod6) Formula: resp ~ expt01 * (b0 + exp(b1 + b22 * log(dose))) * exp(-b3 * dose) + (1 - expt01) * (b0 + exp(b1 + b21 * log(dose))) * exp(-b3 * dose) Parameters: Estimate Std. Error t value Pr(>|t|) b0 22.19882 1.92870 11.51 8.68e-14 *** b1 7.21646 0.02679 269.39 < 2e-16 *** b21 1.00077 0.02134 46.90 < 2e-16 *** b3 0.26243 0.01731 15.16 < 2e-16 *** b22 1.14780 0.03154 36.40 < 2e-16 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 1.062 on 37 degrees of freedom Number of iterations to convergence: 7 Achieved convergence tolerance: 3.042e-06 > deviance(salm.mod6) [1] 41.75144 > > salm.mod7 <- nls(resp ~ expt01*(b02+exp(b1+b2*log(dose)))*exp(-b3*dose) + + (1-expt01)*(b01+exp(b1+b2*log(dose)))*exp(-b3*dose), + start=c(b01=20,b1=10,b2=1,b3=1,b02=20), + weight=varwt,data=salmonella) > summary(salm.mod7) Formula: resp ~ expt01 * (b02 + exp(b1 + b2 * log(dose))) * exp(-b3 * dose) + (1 - expt01) * (b01 + exp(b1 + b2 * log(dose))) * exp(-b3 * dose) Parameters: Estimate Std. Error t value Pr(>|t|) b01 26.57513 3.61867 7.344 9.92e-09 *** b1 7.19485 0.03773 190.673 < 2e-16 *** b2 1.02515 0.03191 32.124 < 2e-16 *** b3 0.25670 0.02483 10.340 1.83e-12 *** b02 17.83804 3.84217 4.643 4.23e-05 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 1.499 on 37 degrees of freedom Number of iterations to convergence: 7 Achieved convergence tolerance: 5.954e-06 > deviance(salm.mod7) [1] 83.12013 > > salm.mod8 <- nls(resp ~ expt01*(b0+exp(b12+b2*log(dose)))*exp(-b3*dose) + + (1-expt01)*(b0+exp(b11+b2*log(dose)))*exp(-b3*dose), + start=c(b0=20,b11=10,b2=1,b3=1,b12=10), + weight=varwt,data=salmonella) > summary(salm.mod8) Formula: resp ~ expt01 * (b0 + exp(b12 + b2 * log(dose))) * exp(-b3 * dose) + (1 - expt01) * (b0 + exp(b11 + b2 * log(dose))) * exp(-b3 * dose) Parameters: Estimate Std. Error t value Pr(>|t|) b0 22.43499 2.78095 8.067 1.13e-09 *** b11 7.21708 0.04910 146.975 < 2e-16 *** b2 1.02422 0.03352 30.555 < 2e-16 *** b3 0.26220 0.02809 9.335 2.90e-11 *** b12 7.18701 0.03805 188.892 < 2e-16 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 1.532 on 37 degrees of freedom Number of iterations to convergence: 8 Achieved convergence tolerance: 2.393e-06 > deviance(salm.mod8) [1] 86.86501 > > salm.mod9 <- nls(resp ~ expt01*(b02+exp(b1+b2*log(dose)))*exp(-b32*dose) + + (1-expt01)*(b01+exp(b1+b2*log(dose)))*exp(-b31*dose), + start=c(b01=20,b1=10,b2=1,b31=1,b02=20,b32=1), + weight=varwt,data=salmonella) > summary(salm.mod9) Formula: resp ~ expt01 * (b02 + exp(b1 + b2 * log(dose))) * exp(-b32 * dose) + (1 - expt01) * (b01 + exp(b1 + b2 * log(dose))) * exp(-b31 * dose) Parameters: Estimate Std. Error t value Pr(>|t|) b01 26.91948 3.51345 7.662 4.54e-09 *** b1 7.16999 0.03864 185.560 < 2e-16 *** b2 1.01423 0.03143 32.266 < 2e-16 *** b31 0.24856 0.02433 10.217 3.49e-12 *** b02 17.39181 3.73125 4.661 4.21e-05 *** b32 0.21944 0.03063 7.164 2.00e-08 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 1.453 on 36 degrees of freedom Number of iterations to convergence: 7 Achieved convergence tolerance: 5.277e-06 > deviance(salm.mod9) [1] 76.03964 > > anova(salm.mod3,salm.mod4) Analysis of Variance Table Model 1: resp ~ (b0 + exp(b1 + b2 * log(dose))) * exp(-b3 * dose) Model 2: resp ~ expt01 * (b02 + exp(b12 + b22 * log(dose))) * exp(-b32 * dose) + (1 - expt01) * (b01 + exp(b11 + b21 * log(dose))) * exp(-b31 * dose) Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F) 1 38 89.713 2 34 38.999 4 50.713 11.053 7.501e-06 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 > anova(salm.mod5,salm.mod4) Analysis of Variance Table Model 1: resp ~ expt01 * (b02 + exp(b1 + b22 * log(dose))) * exp(-b3 * dose) + (1 - expt01) * (b01 + exp(b1 + b21 * log(dose))) * exp(-b3 * dose) Model 2: resp ~ expt01 * (b02 + exp(b12 + b22 * log(dose))) * exp(-b32 * dose) + (1 - expt01) * (b01 + exp(b11 + b21 * log(dose))) * exp(-b31 * dose) Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F) 1 36 40.890 2 34 38.999 2 1.8909 0.8243 0.4471 > anova(salm.mod6,salm.mod4) Analysis of Variance Table Model 1: resp ~ expt01 * (b0 + exp(b1 + b22 * log(dose))) * exp(-b3 * dose) + (1 - expt01) * (b0 + exp(b1 + b21 * log(dose))) * exp(-b3 * dose) Model 2: resp ~ expt01 * (b02 + exp(b12 + b22 * log(dose))) * exp(-b32 * dose) + (1 - expt01) * (b01 + exp(b11 + b21 * log(dose))) * exp(-b31 * dose) Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F) 1 37 41.751 2 34 38.999 3 2.7524 0.7999 0.5026 > anova(salm.mod7,salm.mod4) Analysis of Variance Table Model 1: resp ~ expt01 * (b02 + exp(b1 + b2 * log(dose))) * exp(-b3 * dose) + (1 - expt01) * (b01 + exp(b1 + b2 * log(dose))) * exp(-b3 * dose) Model 2: resp ~ expt01 * (b02 + exp(b12 + b22 * log(dose))) * exp(-b32 * dose) + (1 - expt01) * (b01 + exp(b11 + b21 * log(dose))) * exp(-b31 * dose) Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F) 1 37 83.120 2 34 38.999 3 44.121 12.822 9.178e-06 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 > anova(salm.mod8,salm.mod4) Analysis of Variance Table Model 1: resp ~ expt01 * (b0 + exp(b12 + b2 * log(dose))) * exp(-b3 * dose) + (1 - expt01) * (b0 + exp(b11 + b2 * log(dose))) * exp(-b3 * dose) Model 2: resp ~ expt01 * (b02 + exp(b12 + b22 * log(dose))) * exp(-b32 * dose) + (1 - expt01) * (b01 + exp(b11 + b21 * log(dose))) * exp(-b31 * dose) Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F) 1 37 86.865 2 34 38.999 3 47.866 13.91 4.413e-06 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 > anova(salm.mod9,salm.mod4) Analysis of Variance Table Model 1: resp ~ expt01 * (b02 + exp(b1 + b2 * log(dose))) * exp(-b32 * dose) + (1 - expt01) * (b01 + exp(b1 + b2 * log(dose))) * exp(-b31 * dose) Model 2: resp ~ expt01 * (b02 + exp(b12 + b22 * log(dose))) * exp(-b32 * dose) + (1 - expt01) * (b01 + exp(b11 + b21 * log(dose))) * exp(-b31 * dose) Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F) 1 36 76.040 2 34 38.999 2 37.041 16.146 1.176e-05 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 >