Why does my nonlinear regression curve have straight line segments?-CodePudding

I try to draw a non-linear curve but I don't know why it has straight line segements. The original data is as below:

ISIDOR <- structure(list(Pos_heliaphen = c("W30", "X41", "Y27", "Z24", 
                                       "Y27", "W30", "W30", "X41", "Y27", "W30", "X41", "Z40", "Z99"
), traitement = c("WW", "WW", "WW", "WW", "WW", "WW", "WW", "WW", 
                  "WW", "WW", "WW", "WW", "WW"), Variete = c("Isidor", "Isidor", 
                                                             "Isidor", "Isidor", "Isidor", "Isidor", "Isidor", "Isidor", "Isidor", 
                                                             "Isidor", "Isidor", "Isidor", "Cali"), FTSW_apres_arros = c(0.462837958498518, 
                                                                                                                         0.400045032939416, 0.352560790392534, 0.377856799586057, 0.170933345859364, 
                                                                                                                         0.315689846065931, 0.116825600914318, 0.0332444780173884, 0.00966070114456602, 
                                                                                                                         0.0871102539376406, 0.0107280083093036, 0.195548432729584, 1), 
NLE = c(0.903498791068124, 0.954670066942938, 0.970762905436272, 
        0.873838605282389, 0.647875257025359, 0.53056603773585, 0.0384548155916796, 
        0.0470924009989314, 0.00403163281128882, 0.193696514297641, 
        0.0718450645564359, 0.295346695941639, 1)), class = c("tbl_df", 
                                                              "tbl", "data.frame"), row.names = c(NA, -13L))

And here is the code:

mod = nls(NLE ~ 2/(1 exp(a*FTSW_apres_arros))-1,start = list(a=1),data = ISIDOR)
ISIDOR$pred = predict(mod,ISIDOR)
a = coef(mod)
RMSE = rmse(ISIDOR$NLE, ISIDOR$pred)
MSE = mse(ISIDOR$NLE, ISIDOR$pred)
Rsquared = summary(lm(ISIDOR$NLE~ ISIDOR$pred))$r.squared


  ggplot(ISIDOR,aes(x=FTSW_apres_arros))   
  geom_point(aes(y=NLE,color=Variete), pch=19, cex=3)  
  scale_color_manual(values = c("red3","blue3")) 
  geom_line(aes(y=pred), color="black", lwd=1.2)  
  scale_y_continuous(limits = c(0,1.0))  
  scale_x_continuous(limits = c(0,1))  
  labs(title = "Isidor", y="Expansion folliaire totale relative",x="FTSW",
       subtitle = paste0("y = 2/(1   exp(",round(a,3), "* x)) -1)","\n",
                         "R^2 = ", round(Rsquared,3),"  RMSE = ", round(RMSE,3),"   MSE = ", round(MSE,3))) 
  theme(plot.title = element_text(hjust = 0,size=14, face = "bold", colour = "black"),
        plot.subtitle = element_text(hjust = 0,size=10, face = "italic", colour = "black"),
        legend.position = "none")

And here is the final figure:

You can at the end of the curve, there is a straight line, which doesn't respect the non-linear equation calculated in the the figure.

Can anyone help me? Thank you in advance!

CodePudding user response：

You are only predicting at the x values already present in your data. The resulting predictions are joined up by straight lines. You need to feed the predict function the sequence of x values at which to predict. If you give it lots of points evenly spaced across your x axis, you get a smooth line. It's best to create a little prediction data frame for this purpose:

pred_df <- data.frame(FTSW_apres_arros = seq(min(ISIDOR$FTSW_apres_arros), 
                                         max(ISIDOR$FTSW_apres_arros),
                                         length.out = 100))

pred_df$NLE <- predict(mod, newdata = pred_df)

And now we pass this data frame to the data argument of geom_line

ggplot(ISIDOR, aes(FTSW_apres_arros, NLE))   
  geom_point(aes(color = Variete), pch = 19, cex = 3)  
  geom_line(data = pred_df)  
  scale_color_manual(values = c("red3","blue3")) 
  scale_y_continuous(limits = c(0, 1.0))  
  scale_x_continuous(limits = c(0, 1))  
  labs(title = "Isidor", 
       y = "Expansion folliaire totale relative",
       x = "FTSW",
       subtitle = paste0("y = 2/(1   exp(", round(a, 3), "* x)) -1)","\n",
                         "R^2 = ", round(Rsquared, 3),"  RMSE = ",
                         round(RMSE, 3), "   MSE = ", round(MSE, 3))) 
  theme(plot.title = element_text(hjust = 0, size = 14, face = "bold", 
                                  colour = "black"),
        plot.subtitle = element_text(hjust = 0,size=10, face = "italic", 
                                     colour = "black"),
        legend.position = "none")