Misra1c: Monomolecular Absorption data

In NISTnls: Nonlinear least squares examples from NIST

Description

The Misra1c data frame has 14 rows and 2 columns. This is the same data as Misra1a but a different model is fit.

Format

This data frame contains the following columns:

y

A numeric vector of volume values.

x

A numeric vector of pressure values.

Details

These data are the result of a NIST study regarding dental research in monomolecular adsorption. The response variable is volume, and the predictor variable is pressure.

Source

Misra, D., NIST (1978). Dental Research Monomolecular Adsorption Study.

Examples

Try <- function(expr) if (!inherits(val <- try(expr), "try-error")) val
plot(y ~ x, data = Misra1c)
Try(fm1 <- nls(y ~ b1*(1-(1+2*b2*x)**(-.5)), data = Misra1c, trace = TRUE,
           start = c(b1 = 500, b2 = 0.0001) ))
Try(fm1a <- nls(y ~ b1*(1-(1+2*b2*x)**(-.5)), data = Misra1c, trace = TRUE,
           alg = "port", start = c(b1 = 500, b2 = 0.0001) ))
Try(fm2 <- nls(y ~ b1*(1-(1+2*b2*x)**(-.5)), data = Misra1c, trace = TRUE,
           start = c(b1 = 600, b2 = 0.0002) ))
Try(fm2a <- nls(y ~ b1*(1-(1+2*b2*x)**(-.5)), data = Misra1c, trace = TRUE,
           alg = "port", start = c(b1 = 600, b2 = 0.0002) ))
Try(fm3 <- nls(y ~ 1-(1+2*b2*x)**(-.5), data = Misra1c, trace = TRUE,
           start = c(b2 = 0.0001), algorithm = "plinear" ))
Try(fm4 <- nls(y ~ 1-(1+2*b2*x)**(-.5), data = Misra1c, trace = TRUE,
           start = c(b2 = 0.0002), algorithm = "plinear" ))

Example output

11603.02 :  5e+02 1e-04
8452.255 :  2.973034e+02 2.223794e-04
138.0325 :  6.344276e+02 1.933620e-04
0.05964058 :  6.337918e+02 2.089646e-04
0.04097522 :  6.364150e+02 2.081371e-04
0.04096684 :  6.364273e+02 2.081363e-04
Nonlinear regression model
  model: y ~ b1 * (1 - (1 + 2 * b2 * x)^(-0.5))
   data: Misra1c
       b1        b2 
6.364e+02 2.081e-04 
 residual sum-of-squares: 0.04097

Number of iterations to convergence: 5 
Achieved convergence tolerance: 1.222e-06
  0:     5801.5082:  500.000 0.000100000
  1:     522.80178:  831.329 0.000184686
  2:     12.564879:  629.050 0.000204239
  3:   0.020834412:  636.280 0.000208227
  4:   0.020483419:  636.427 0.000208136
  5:   0.020483418:  636.427 0.000208136
  6:   0.020483418:  636.427 0.000208136
Nonlinear regression model
  model: y ~ b1 * (1 - (1 + 2 * b2 * x)^(-0.5))
   data: Misra1c
       b1        b2 
6.364e+02 2.081e-04 
 residual sum-of-squares: 0.04097

Algorithm "port", convergence message: both X-convergence and relative convergence (5)
262.4566 :  6e+02 2e-04
0.1559867 :  6.357031e+02 2.088635e-04
0.0409676 :  6.364173e+02 2.081389e-04
0.04096684 :  6.364272e+02 2.081363e-04
Nonlinear regression model
  model: y ~ b1 * (1 - (1 + 2 * b2 * x)^(-0.5))
   data: Misra1c
       b1        b2 
6.364e+02 2.081e-04 
 residual sum-of-squares: 0.04097

Number of iterations to convergence: 3 
Achieved convergence tolerance: 1.091e-06
  0:     131.22829:  600.000 0.000200000
  1:     9.2635332:  620.165 0.000208610
  2:   0.020527623:  636.422 0.000208126
  3:   0.020483418:  636.427 0.000208136
  4:   0.020483418:  636.427 0.000208136
Nonlinear regression model
  model: y ~ b1 * (1 - (1 + 2 * b2 * x)^(-0.5))
   data: Misra1c
       b1        b2 
6.364e+02 2.081e-04 
 residual sum-of-squares: 0.04097

Algorithm "port", convergence message: relative convergence (4)
14.7926 :     0.0001 1226.0429
0.1176382 :  1.997722e-04 6.593247e+02
0.04097147 :  2.080709e-04 6.365991e+02
0.04096684 :  2.081361e-04 6.364277e+02
0.04096684 :  2.081363e-04 6.364273e+02
Nonlinear regression model
  model: y ~ 1 - (1 + 2 * b2 * x)^(-0.5)
   data: Misra1c
       b2      .lin 
2.081e-04 6.364e+02 
 residual sum-of-squares: 0.04097

Number of iterations to convergence: 4 
Achieved convergence tolerance: 2.155e-06
0.1134958 :    0.0002 658.6757
0.04097105 :  2.080739e-04 6.365911e+02
0.04096684 :  2.081361e-04 6.364276e+02
0.04096684 :  2.081363e-04 6.364273e+02
Nonlinear regression model
  model: y ~ 1 - (1 + 2 * b2 * x)^(-0.5)
   data: Misra1c
       b2      .lin 
2.081e-04 6.364e+02 
 residual sum-of-squares: 0.04097

Number of iterations to convergence: 3 
Achieved convergence tolerance: 1.44e-06

NISTnls documentation built on May 2, 2019, 2:37 a.m.