# Detailed Information of Estimated Model Parameters Provides the estimates, standard errors, confidence intervals, Jacobian matrix, and the covariance matrix of model parameters. ```r parinfo(object, x, CI = 0.95, tol = 1e-30, 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) - `tol`: The tolerance for detecting linear dependencies in the columns of a matrix in the QR decomposition. See the input argument of `tol` of the `qr` function in package `base` - `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. ## Returns - **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 ## References Bates, D.M and Watts, D.G. (1988) **Nonlinear Regression Analysis and its Applications**. Wiley, New York. tools:::Rd_expr_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. ## Author(s) Peijian Shi pjshi@njfu.edu.cn , Peter M. Ridland p.ridland@unimelb.edu.au , David A. Ratkowsky d.ratkowsky@utas.edu.au , Yang Li yangli@fau.edu . ## 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`. ## See Also `biasIPEC`, `confcurves`, `curvIPEC`, `skewIPEC`, `hessian` in package `numDeriv`, `jacobian` in package `numDeriv` ## Examples ```r #### 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() ```

parinfo function