Merge branch 'SSmodel-examples'

Author: jarioksa

man/SSarrhenius.Rd

@@ -32,6 +32,11 @@ SSlomolino(area, Asym, xmid, slope)
   }
 }
 \details{
+  These functions are intended to be used as self-starting models in
+  non-linear regression (\code{\link{nls}}). There are several functions
+  that can be used to further handle \code{nls} result, including
+  \code{summary}, \code{confint} and many more (see \code{\link{nls}}).
+
   All these functions are assumed to be used for species richness
   (number of species) as the independent variable, and area or sample
   size as the independent variable. Basically, these define least
@@ -73,7 +78,10 @@ SSlomolino(area, Asym, xmid, slope)
   Numeric vector of the same length as \code{area}. It is the value of
   the expression of each model. If all arguments are names of objects
   the gradient matrix with respect to these names is attached as an
-  attribute named \code{gradient}. 
+  attribute named \code{gradient}. This result object will be used in
+  non-linear regression in function \code{\link{nls}} which returns its
+  own result object with many support functions documented with
+  \code{\link{nls}}.
 }
 \references{
   Dengler, J. (2009) Which function describes the species-area
@@ -105,6 +113,7 @@ plot(S ~ area, sipoo.map,  xlab = "Island Area (ha)",
 ## The Arrhenius model
 marr <- nls(S ~ SSarrhenius(area, k, z), data=sipoo.map)
 marr
+summary(marr)
 ## confidence limits from profile likelihood
 confint(marr)
 ## draw a line
@@ -113,7 +122,7 @@ lines(xtmp, predict(marr, newdata=data.frame(area = xtmp)), lwd=2)
 ## The normal way is to use linear regression on log-log data,
 ## but this will be different from the previous:
 mloglog <- lm(log(S) ~ log(area), data=sipoo.map)
-mloglog
+summary(mloglog) # (Intercept) is log(k) of SSarrhenius result
 lines(xtmp, exp(predict(mloglog, newdata=data.frame(area=xtmp))),
    lty=2)
 ## Gleason: log-linear
@@ -126,7 +135,7 @@ lines(xtmp, predict(mgit, newdata=data.frame(area=xtmp)),
   lwd=2, col = 3)
 ## Lomolino: using original names of the parameters (Lomolino 2000):
 mlom <- nls(S ~ SSlomolino(area, Smax, A50, Hill), sipoo.map)
-mlom
+summary(mlom)
 lines(xtmp, predict(mlom, newdata=data.frame(area=xtmp)),
   lwd=2, col = 4)
 ## One canned model of standard R:

tests/Examples/vegan-Ex.Rout.save

@@ -411,6 +411,22 @@ Nonlinear regression model
 
 Number of iterations to convergence: 5 
 Achieved convergence tolerance: 1.056e-06
+> summary(marr)
+
+Formula: S ~ SSarrhenius(area, k, z)
+
+Parameters:
+  Estimate Std. Error t value Pr(>|t|)    
+k  3.40619    0.40790   8.351 3.16e-07 ***
+z  0.43644    0.02743  15.910 3.15e-11 ***
+---
+Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
+
+Residual standard error: 2.209 on 16 degrees of freedom
+
+Number of iterations to convergence: 5 
+Achieved convergence tolerance: 1.056e-06
+
 > ## confidence limits from profile likelihood
 > confint(marr)
 Waiting for profiling to be done...
@@ -423,14 +439,25 @@ z 0.3813576 0.4944693
 > ## The normal way is to use linear regression on log-log data,
 > ## but this will be different from the previous:
 > mloglog <- lm(log(S) ~ log(area), data=sipoo.map)
-> mloglog
+> summary(mloglog) # (Intercept) is log(k) of SSarrhenius result
 
 Call:
 lm(formula = log(S) ~ log(area), data = sipoo.map)
 
+Residuals:
+     Min       1Q   Median       3Q      Max 
+-0.87519 -0.11897  0.05503  0.19842  0.40087 
+
 Coefficients:
-(Intercept)    log(area)  
-     1.0111       0.4925  
+            Estimate Std. Error t value Pr(>|t|)    
+(Intercept)  1.01109    0.14897   6.787 4.36e-06 ***
+log(area)    0.49252    0.05565   8.850 1.46e-07 ***
+---
+Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
+
+Residual standard error: 0.3163 on 16 degrees of freedom
+Multiple R-squared:  0.8304,	Adjusted R-squared:  0.8198 
+F-statistic: 78.32 on 1 and 16 DF,  p-value: 1.462e-07
 
 > lines(xtmp, exp(predict(mloglog, newdata=data.frame(area=xtmp))),
 +    lty=2)
@@ -444,16 +471,23 @@ Coefficients:
 +   lwd=2, col = 3)
 > ## Lomolino: using original names of the parameters (Lomolino 2000):
 > mlom <- nls(S ~ SSlomolino(area, Smax, A50, Hill), sipoo.map)
-> mlom
-Nonlinear regression model
-  model: S ~ SSlomolino(area, Smax, A50, Hill)
-   data: sipoo.map
-  Smax    A50   Hill 
-53.493 94.697  2.018 
- residual sum-of-squares: 55.37
+> summary(mlom)
+
+Formula: S ~ SSlomolino(area, Smax, A50, Hill)
+
+Parameters:
+     Estimate Std. Error t value Pr(>|t|)    
+Smax   53.493     13.849   3.863  0.00153 ** 
+A50    94.697     74.964   1.263  0.22578    
+Hill    2.018      0.235   8.587 3.56e-07 ***
+---
+Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
+
+Residual standard error: 1.921 on 15 degrees of freedom
 
 Number of iterations to convergence: 6 
 Achieved convergence tolerance: 9.715e-07
+
 > lines(xtmp, predict(mlom, newdata=data.frame(area=xtmp)),
 +   lwd=2, col = 4)
 > ## One canned model of standard R:
@@ -9177,7 +9211,7 @@ Procrustes sum of squares:
 > cleanEx()
 > options(digits = 7L)
 > base::cat("Time elapsed: ", proc.time() - base::get("ptime", pos = 'CheckExEnv'),"\n")
-Time elapsed:  8.784 0.398 9.198 0 0 
+Time elapsed:  8.8 0.411 9.234 0 0 
 > grDevices::dev.off()
 null device 
           1