Non-Linear Regressions

General
1

For a Fisheries Research class project, I am using R to get p-values for linear and non-linear regressions. I have successfully gotten p-values for linear and logarithmic regressions, and the equations matched the regressions I did in excel to check.

Despite some success, I have had some troubles with exponential and power function regressions. I have gotten outputs for both, but the estimated parameters are very different from the ones I got in Excel. I've included the code that I've been using for each regression type below.

As additional context, I am doing regressions with percent brown trout (p_brown) on the y axis and environmental conditions on the x axis. I have named the environmental conditions as follows: season_condition_extreme. For example, fa_d_max would correspond to fall_discharge_maximum.

Linear (works & matches Excel)

plot(p_brown~fa_d_max)
linreg_fa_d_max <- lm(p_brown~fa_d_max)
abline(linreg_fa_d_max)
summary(linreg_fa_d_max)

Logarithmic (works & matches Excel)

plot(p_brown~su_d_max)
logreg_su_d_max <- nls(p_brown~a*log(su_d_max)+b,
                       start = list(a = 4, b = -2))
summary(logreg_su_d_max)

Exponential (works, but doesn't match Excel)
Excel regression: y = 5.6287 * e^(0.0325​ * x)
R regression: y = 7.248 * e^(0.0271 * x)

plot(p_brown~sp_d_min)
expreg_sp_d_min <- nls(p_brown~a*exp(b*sp_d_min),
                       start = list(a = 5, b = 0))
summary(expreg_sp_d_min)

Power (works, but doesn't match Excel)
Excel regression: y = 3.4559 * x^(0.4272)
R regression: y = 7.5279 * x^(0.2282)

plot(p_brown~fa_d_min)
powreg_fa_d_min <- nls(p_brown~a*(fa_d_min^(b)),
                       start = list(a = 3.5, b = .4))
summary(powreg_fa_d_min)

I appreciate any help or pointers that I can get. My experience in R is minimal, so this is all very new to me. Thanks!

2

Can you provide a reproducible example?

3

Have you compared performance metrics/residuals to form an opinion of whether the excel solutions are preffered to your nls solutions?

4

Here is a test dataset to use for each regression type. I've included a screenshot of the Excel output that I get from it.

tibble::tribble(
    ~env_cond,    ~p_fish,
40.35139752, 34.93150685,
 28.4673913, 21.70564746,
40.75807453, 24.90221643,
36.28462733, 7.305936073,
28.01552795, 13.32464571,
36.32981366, 15.70881226,
30.68152174, 8.983890954,
30.18447205, 18.71401152
)
#> # A tibble: 8 x 2
#>   env_cond p_fish
#>    <dbl>   <dbl>
#> 1   40.4   34.9 
#> 2   28.5   21.7 
#> 3   40.8   24.9 
#> 4   36.3    7.31
#> 5   28.0   13.3 
#> 6   36.3   15.7 
#> 7   30.7    8.98
#> 8   30.2   18.7

Screen Shot 2020-11-19 at 8.07.58 AM
Screen Shot 2020-11-19 at 8.07.58 AM1518×1030 128 KB

5

I just compared the Residual Standard Errors of one of the power functions in Excel vs R. The RSE for R was 8.416 and 6.168 in Excel.

6

How does the data that you have provided relate to the code that you initially posted?

7

After some more digging, it seems that the difference in results between in Excel and R is due to a difference in regression methodology. The nls() function in R takes a more complex yet direct approach of running a regression on the data, while Excel transforms the data, runs a linear regression, then converts the parameters back into the nonlinear, non-transformed equivalent.

8

My general rule is if there a difference between R and Excel trust R.

Excel will do some strange things sometimes.

9

I am Linex so I cannot check in Excel but, if you do not mind a slightly stupid suggestion, what about trying the regression in the spreadsheet program gnumeric? I know this does not answer the R vs Excel question directly but it is another source of comparison and gnumeric algorithms in regression seem a bit more trustworthy than Excel's.

10

This topic was automatically closed 21 days after the last reply. New replies are no longer allowed.

If you have a query related to it or one of the replies, start a new topic and refer back with a link.