parinfo {IPEC}

Detailed Information of Estimated Model Parameters

Description

Provides the estimates, standard errors, confidence intervals, Jacobian matrix, and the covariance matrix of model parameters.

Usage

parinfo(object, x, CI = 0.95, method = "Richardson", 
        method.args = list(eps = 1e-04, d = 0.11, 
        zero.tol = sqrt(.Machine$double.eps/7e-07), r = 6, 
        v = 2, show.details = FALSE), side = NULL)

Arguments

object

A fitted model object for which there exist the model expression(expr), the sample size (sample.size or n), estimate(s) of model parameter(s) (par), and residual sum of squares (RSS)

x

A vector or a matrix of observations of independent variable(s)

CI

The confidence level(s) of the required interval(s)

method

It is the same as the input argument of method of the hessian function in package numDeriv

method.args

It is the same as the input argument of method.args of the hessian function in package numDeriv

side

It is the same as the input argument of side of the jacobian function in package numDeriv

Details

The object argument cannot be a list. It is a fitted model object from using the fitIPEC function.

Value

D

The Jacobian matrix of model parameters at all the x observations

partab

The estimates, standard errors and confidence intervals of model parameters

covmat

The covariance matrix of model parameters

Note

When there are sample.size and n in object at the same time, the default of the sample size is sample.size, which is superior to n.

Author(s)

Peijian Shi [e-mail], Peter M. Ridland [e-mail], David A. Ratkowsky [e-mail], Yang Li [e-mail].

References

Bates, D.M and Watts, D.G. (1988) Nonlinear Regression Analysis and its Applications. Wiley, New York. doi:10.1002/9780470316757

Ratkowsky, D.A. (1983) Nonlinear Regression Modeling: A Unified Practical Approach. Marcel Dekker, New York.

Ratkowsky, D.A. (1990) Handbook of Nonlinear Regression Models, Marcel Dekker, New York.

See Also

biasIPEC, confcurves, curvIPEC, skewIPEC, hessian in package numDeriv, jacobian in package numDeriv

Examples

#### Example 1 ###################################################################################
# Weight of cut grass data (Pattinson 1981)
# References:
#   Clarke, G.P.Y. (1987) Approximate confidence limits for a parameter function in nonlinear 
#       regression. J. Am. Stat. Assoc. 82, 221-230.
#   Gebremariam, B. (2014) Is nonlinear regression throwing you a curve? 
#       New diagnostic and inference tools in the NLIN Procedure. Paper SAS384-2014.
#       http://support.sas.com/resources/papers/proceedings14/SAS384-2014.pdf
#   Pattinson, N.B. (1981) Dry Matter Intake: An Estimate of the Animal
#       Response to Herbage on Offer. unpublished M.Sc. thesis, University
#       of Natal, Pietermaritzburg, South Africa, Department of Grassland Science.

# 'x4' is the vector of weeks after commencement of grazing in a pasture
# 'y4' is the vector of weight of cut grass from 10 randomly sited quadrants

x4 <- 1:13
y4 <- c(3.183, 3.059, 2.871, 2.622, 2.541, 2.184, 
        2.110, 2.075, 2.018, 1.903, 1.770, 1.762, 1.550)

# Define the first case of Mitscherlich equation
MitA <- function(P1, x){
    P1[3] + P1[2]*exp(P1[1]*x)
}

# Define the second case of Mitscherlich equation
MitB <- function(P2, x){
    log( P2[3] ) + exp(P2[2] + P2[1]*x)
}

# Define the third case of Mitscherlich equation
MitC <- function(P3, x, x1=1, x2=13){
    theta1 <- P3[1]
    beta2  <- P3[2]
    beta3  <- P3[3]
    theta2 <- (beta3 - beta2)/(exp(theta1*x2)-exp(theta1*x1))
    theta3 <- beta2/(1-exp(theta1*(x1-x2))) - beta3/(exp(theta1*(x2-x1))-1)
    theta3 + theta2*exp(theta1*x)
}

ini.val3 <- c(-0.1, 2.5, 1)
r1       <- fitIPEC( MitA, x=x4, y=y4, ini.val=ini.val3, xlim=NULL, ylim=NULL,  
                     fig.opt=TRUE, control=list(
                     trace=FALSE, reltol=1e-20, maxit=50000) )
parA     <- r1$par
parA
result1  <- parinfo(r1, x=x4, CI=0.95)
result1

ini.val4 <- c(-0.10, 0.90, 2.5)
R0       <- fitIPEC( MitB, x=x4, y=y4, ini.val=ini.val4, xlim=NULL, ylim=NULL,  
                     fig.opt=TRUE, control=list(
                     trace=FALSE, reltol=1e-20, maxit=50000) )
parB     <- R0$par
parB
result2  <- parinfo(R0, x=x4, CI=0.95)
result2

ini.val6 <- c(-0.15, 2.52, 1.09)
RES0     <- fitIPEC( MitC, x=x4, y=y4, ini.val=ini.val6, xlim=NULL, ylim=NULL,  
                     fig.opt=TRUE, control=list(trace=FALSE, 
                     reltol=1e-20, maxit=50000) )
parC     <- RES0$par
parC
result3  <- parinfo(RES0, x=x4, CI=0.95)
result3
##################################################################################################


#### Example 2 ###################################################################################
# Data on biochemical oxygen demand (BOD; Marske 1967)
# References:
# Pages 56, 255 and 271 in Bates and Watts (1988)
# Carr, N.L. (1960) Kinetics of catalytic isomerization of n-pentane. Ind. Eng. Chem.
#     52, 391-396.   

data(isom)
Y <- isom[,1]
X <- isom[,2:4]

# There are three independent variables saved in matrix 'X' and one response variable (Y)
# The first column of 'X' is the vector of partial pressure of hydrogen
# The second column of 'X' is the vector of partial pressure of n-pentane
# The third column of 'X' is the vector of partial pressure of isopentane
# Y is the vector of experimental reaction rate (in 1/hr)

isom.fun <- function(theta, x){
  x1     <- x[,1]
  x2     <- x[,2]
  x3     <- x[,3]
  theta1 <- theta[1]
  theta2 <- theta[2]
  theta3 <- theta[3]
  theta4 <- theta[4]
  theta1*theta3*(x2-x3/1.632) / ( 1 + theta2*x1 + theta3*x2 + theta4*x3 )
}

ini.val8 <- c(35, 0.1, 0.05, 0.2)
cons1    <- fitIPEC( isom.fun, x=X, y=Y, ini.val=ini.val8, control=list(
                     trace=FALSE, reltol=1e-20, maxit=50000) )
par8     <- cons1$par 
result2  <- parinfo(cons1, x=X, CI=0.95)
result2
##################################################################################################

graphics.off()