Using Reproducible Research to Revisit Published Results

R4PlantPath Reproducible Research

In which the author revisits a previously published analysis and finds ways to improve it while using reproducible research to illustrate refitting a GAM using random effects to better fit the model to the data.

Adam H. Sparks

Note on Further Refinement

I realised I neglected to explore including the pots at each station and the plants in each pot for the random effects. The mod_new now includes these and the model fit is further improved with their inclusion. -ahs 2024-04-28


I’ve recently just wrapped up an analysis with co-authors looking at the aerial dispersal of peanut smut spores from infested fields in Argentina (Paredes et al. 2024; Edwards Molina, Sparks, and Paredes 2022). In this paper, we used a Generalised Additive Model (GAM) to describe how far the spores spread and what was linked with this in the R programming environment. This model was particularly difficult for me to fit initially due to spatial autocorrelation effects due to the spore trap locations and time-slices that were used to collect the spore counts. It also had six different fields where data were collected. So there were lots of things going on here, six fields, traps on transects in four directions from the centroid with traps located four distances on the transect and the time in which spores were collected overlapped from 0-90, 0-180 and 0-270 minutes.

To deal with all of this I spent lots of time reading up on fitting GAMs, but this time, I was reading about using random effects in the GAM, which is something I’d not done in the past. I used GAMs in the past for work in my PhD dissertation (Sparks et al. 2014; Sparks 2024) and in “The role of conidia in the dispersal of Ascochyta rabiei(Khaliq et al. 2020b, 2020a), which brings me to today’s post.

To handle all of the issues with multiple field sites and the spatio-temporal autocorrelation, I used random effects in my GAM for Paredes et al. (2024). However, I realised I’d not used random effects for this work (Khaliq et al. 2020b, 2020a). So, to rectify this, I thought I’d go back to the published work and see if I could improve my model’s fit to the data using random effects.

As we set up the research compendium as an R package, it’s easy enough to install it and get started working with the data and reproduce the work published in Khaliq et al. (2020b). We assume that you have the R package {devtools} installed, if not, use install.packages("devtools").

Getting Started


Now we can load the data, lesion_counts and summary_weather, from {ChickpeaAscoDispersal} and create the dat object used to fit the GAM in the original paper.

We will use set.seed() here to ensure that the same results are obtained when checking the model fits.1



dat <-
  left_join(lesion_counts, summary_weather, by = c("site", "rep"))

             SpEv                   site     rep        distance    
 Curyo Rain 1  :56   Curyo            : 56   1:168   Min.   : 0.00  
 Horsham Irrg 1:56   Horsham dryland  :112   2:112   1st Qu.:10.00  
 Horsham Irrg 2:56   Horsham irrigated:168   3: 56   Median :25.00  
 Horsham Mixd 1:56                                   Mean   :32.68  
 Horsham Rain 1:56                                   3rd Qu.:50.00  
 Horsham Rain 2:56                                   Max.   :75.00  
    station          transect       plant_no         pot_no     
 Min.   : 1.000   Min.   : 1.0   Min.   :3.000   Min.   : 1.00  
 1st Qu.: 2.000   1st Qu.: 3.0   1st Qu.:3.000   1st Qu.:14.75  
 Median : 4.000   Median : 5.5   Median :5.000   Median :28.50  
 Mean   : 4.643   Mean   : 5.5   Mean   :4.286   Mean   :28.50  
 3rd Qu.: 7.000   3rd Qu.: 8.0   3rd Qu.:5.000   3rd Qu.:42.25  
 Max.   :10.000   Max.   :10.0   Max.   :5.000   Max.   :56.00  
   counts_p1        counts_p2       counts_p3        counts_p4     
 Min.   : 0.000   Min.   :0.000   Min.   : 0.000   Min.   : 0.000  
 1st Qu.: 0.000   1st Qu.:0.000   1st Qu.: 0.000   1st Qu.: 0.000  
 Median : 1.000   Median :0.000   Median : 0.000   Median : 1.000  
 Mean   : 1.243   Mean   :1.021   Mean   : 1.096   Mean   : 1.406  
 3rd Qu.: 2.000   3rd Qu.:2.000   3rd Qu.: 2.000   3rd Qu.: 2.000  
 Max.   :12.000   Max.   :8.000   Max.   :11.000   Max.   :11.000  
 NA's   :2        NA's   :2       NA's   :2        NA's   :124     
   counts_p5         degrees         ptype             m_lesions     
 Min.   : 0.000   Min.   : 10.0   Length:336         Min.   :0.0000  
 1st Qu.: 0.000   1st Qu.: 65.0   Class :character   1st Qu.:0.3333  
 Median : 1.000   Median : 95.0   Mode  :character   Median :0.6667  
 Mean   : 1.333   Mean   :118.0                      Mean   :1.0802  
 3rd Qu.: 2.000   3rd Qu.:127.5                      3rd Qu.:1.4000  
 Max.   :14.000   Max.   :360.0                      Max.   :8.4000  
 NA's   :132                                         NA's   :2       
      mws            ws_sd            mwd           sum_rain   
 Min.   :1.903   Min.   :0.905   Min.   :234.7   Min.   : 0.8  
 1st Qu.:2.233   1st Qu.:1.290   1st Qu.:272.7   1st Qu.: 4.6  
 Median :3.331   Median :2.031   Median :321.7   Median :11.0  
 Mean   :3.554   Mean   :1.867   Mean   :306.3   Mean   : 9.6  
 3rd Qu.:3.996   3rd Qu.:2.230   3rd Qu.:333.7   3rd Qu.:11.6  
 Max.   :6.532   Max.   :2.713   Max.   :353.5   Max.   :18.6  

Fitting the GAMs

With the data now loaded in our R session, we can fit the original GAM as published for us to compare against and see if we can’t improve it.

Original GAM

First, fit the original model as published.


mod_org <-
    m_lesions ~ s(distance, k = 5) +
      s(mws, k = 5) +
      s(sum_rain, k = 5),
    data = dat,
    family = tw()


Family: Tweedie(p=1.044) 
Link function: log 

m_lesions ~ s(distance, k = 5) + s(mws, k = 5) + s(sum_rain, 
    k = 5)

Parametric coefficients:
            Estimate Std. Error t value     Pr(>|t|)    
(Intercept) -0.22823    0.04098  -5.569 0.0000000539 ***
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Approximate significance of smooth terms:
              edf Ref.df       F              p-value    
s(distance) 3.496  3.855 123.776 < 0.0000000000000002 ***
s(mws)      1.992  2.092   0.824              0.45080    
s(sum_rain) 2.812  2.879   5.493              0.00168 ** 
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

R-sq.(adj) =  0.674   Deviance explained = 61.2%
-REML = 309.96  Scale est. = 0.36397   n = 334

New GAM With Random Effects

Now fit a model with random effects for the site (Curyo or Horsham), rep (3) and station (10 per each of 10 transects), pot number and plant number to see if it improves the model fit to the data.

mod_new <-
    m_lesions ~ s(distance, k = 5) +
      s(mws, k = 5) +
      s(sum_rain, k = 5) +
      s(site, rep, station, pot_no, plant_no, bs = "re"),
    data = dat,
    family = tw()


Family: Tweedie(p=1.043) 
Link function: log 

m_lesions ~ s(distance, k = 5) + s(mws, k = 5) + s(sum_rain, 
    k = 5) + s(site, rep, station, pot_no, plant_no, bs = "re")

Parametric coefficients:
            Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.08424    0.06155  -1.369    0.172

Approximate significance of smooth terms:
                                      edf Ref.df      F
s(distance)                         3.650  3.924 65.908
s(mws)                              1.919  2.049  1.997
s(sum_rain)                         2.797  2.878  5.440
s(site,rep,station,pot_no,plant_no) 4.924  6.000  4.058
s(distance)                         < 0.0000000000000002 ***
s(mws)                                           0.29429    
s(sum_rain)                                      0.00125 ** 
s(site,rep,station,pot_no,plant_no)            0.0000601 ***
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

R-sq.(adj) =   0.71   Deviance explained = 64.5%
-REML = 301.99  Scale est. = 0.36131   n = 334

Here we’ve added a new line, s(site, rep, station, pot_no, plant_no, bs = "re") for the random effects. This indicates that we now have a smoothed term for ‘site’, ‘rep’ (replicate), and ‘station’ with bs = "re", where the basis (bs) for the smooth is a random effect (re).

We can see that the \(R^2\) value has increased, 0.7099145 vs 0.6737655 and that the deviance explained has also increased, 64.5% vs 61.2%.

In the original paper, we used AIC to compare models to ensure we didn’t over fit and used the most parsimonious model possible. As we’ve added new terms it’s best to check to ensure that we’ve not added unnecessary complexity to the model.

Compare AIC Values


models <- list(mod_org = mod_org,
               mod_new = mod_new

mod_aic <- map_df(models, glance,
                  .id = "model") %>%

# A tibble: 2 × 8
  model      df logLik   AIC   BIC deviance df.residual  nobs
  <chr>   <dbl>  <dbl> <dbl> <dbl>    <dbl>       <dbl> <int>
1 mod_new 14.3   -271.  578.  645.     129.        320.   334
2 mod_org  9.30  -288.  599.  644.     141.        325.   334

The AIC does improve with the new model, 578 to the original’s, 599, enough to likely warrant the added complexity to the model I’d say. It is of note that the BIC is larger for the new model, 645, to the original’s, 644, so further diagnostics should be used as we did in the paper.

Check Using Model Fit With Descriptive Statistics and Figures

Lastly, we can use gam.check() as in the paper to evaluate the models fitness.

Original Khaliq et al. Model


Method: REML   Optimizer: outer newton
full convergence after 8 iterations.
Gradient range [-0.0000004288943,0.0000002610557]
(score 309.9554 & scale 0.3639671).
Hessian positive definite, eigenvalue range [0.3685077,2978.832].
Model rank =  13 / 13 

Basis dimension (k) checking results. Low p-value (k-index<1) may
indicate that k is too low, especially if edf is close to k'.

              k'  edf k-index p-value  
s(distance) 4.00 3.50    0.87   0.025 *
s(mws)      4.00 1.99    0.98   0.535  
s(sum_rain) 4.00 2.81    1.00   0.625  
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Updated Model With Random Effects


Method: REML   Optimizer: outer newton
full convergence after 10 iterations.
Gradient range [-0.00007401781,0.00003895846]
(score 301.9894 & scale 0.3613127).
Hessian positive definite, eigenvalue range [0.3078677,2958.934].
Model rank =  22 / 22 

Basis dimension (k) checking results. Low p-value (k-index<1) may
indicate that k is too low, especially if edf is close to k'.

                                      k'  edf k-index p-value
s(distance)                         4.00 3.65    0.91    0.13
s(mws)                              4.00 1.92    1.04    0.88
s(sum_rain)                         4.00 2.80    1.05    0.91
s(site,rep,station,pot_no,plant_no) 9.00 4.92      NA      NA

The original model’s “distance” term \(k-index\) was a bit iffy as it was indicated to be significant, but otherwise acceptable for what we wanted as we weren’t forward predicting, just explaining what happened at our trial sites. It indicated that the \(k\) value was too low, which is fair, we only had \(k = 5\) due to a lack of degrees of freedom. Adding the random effects increased the estimated degrees of freedom available and resulted in a better fitting model in the new model’s form with random effects included.

The qq-plot and other diagnostics for the new model also show a slight visual improvement over the original model. Especially the response vs. predicted variables showing much less of a pattern.


In conclusion, this was a fun little exercise that allowed me to explore some new things I’ve learned along the way and apply them to some older work very easily. This isn’t worth going back to the original paper and making any changes as it doesn’t change the story one bit. However, it is nice to see that I was able to take the original work and so easily reproduce it and then upgrade it and confirm what I thought and will be useful information for future work.

Further Resources

Here’s a few more resources that are useful for GAMs.

Edwards Molina, Juan, Adam Sparks, and Juan Paredes. 2022. “Research Compendium: Aerial Dispersion of Smut Spores During Peanut Harvest.”
Khaliq, Ihsanul, Joshua Fanning, Paul Melloy, Jean Galloway, Kevin Moore, Daniel Burrell, and Adam H. Sparks. 2020a. “Raw Data for "The role of conidia in the dispersal of Ascochyta rabiei".” Zenodo.
———. 2020b. “The Role of Conidia in the Dispersal of Ascochyta Rabiei.” European Journal of Plant Pathology 158 (4): 911–24.
Paredes, Juan A., Adam H. Sparks, Joaquín H. Monguillot, Alejandro M. Rago, and Juan. P. Edwards Molina. 2024. “Aerial Spread of Smut Spores During Peanut Harvest.” Tropical Plant Pathology, March.
Sparks, Adam H. 2024. “Adamhsparks/Global-Late-Blight-MetaModelling: V1.2.0.” Zenodo.
Sparks, Adam H., Gregory A. Forbes, Robert J. Hijmans, and Karen A. Garrett. 2014. “Climate Change May Have Limited Effect on Global Risk of Potato Late Blight.” Global Change Biology 20 (12): 3621–31.

  1. I also learned something new by writing this blog post. When I started I didn’t realise that gam.check() used random draws to check the fit. In the case of these models, it can make a difference in the significance of the “distance” term. In most cases it’s not significant when checking the fit of the new model, but in some cases it remains significant as with the original model. The seed chosen (at random) does make it insignificant.↩︎



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