Solved – CLMM Output interpretation from R Ordinal

logisticordered-logitr

Problem description
question is at the end:

I am testing to see what factors are responsible for vegetation change over a large landscape over a period of 100 years. The response variable is an ordinal measure of vegetation change describing how different the vegetation is in terms of its successional state. The response can be 0 (no change), 1 (a little bit of change), 2 (moderate change) or 3 (Maximum change).
Predictors:

I have a model with a random factor (Blockshed: watersheds to control for spatial autocorrelation), an ordered factor (tsf: time since fire)and two continuous variables (Z.elev: standardized elevation; Z.solar : standardized solar insolation).

I am using the CLMM procedure in R:Ordinal package.

Because there are three possible levels of tsf (short, medium, very long), the model tests both linear (L) and quadratic (Q) terms for the variable (n-1 models, if the TSF had 4 levels, it would also test Cubic) . These two models are indicated in the output by TSF.L and TSF.Q. As you will see both are significant, so I would assume I would choose the model with the lowest p-value, or if they are identical (as is the case here), choose the simplest (L) model.

This is the code to run the model:

library(ordinal)
MGall32.clmm <- clmm(chgdir ~ Z.solar + tsf + Z.elev + (1 | blockshed), 
                     data = MG09, Hess = TRUE,
                     control = clmm.control(method = c("nlminb")))

The following is the output from the model:

Question:
what is CLMM doing in the Linear vs Quadratic models? The response variable is an ordered factor with values of 0, 1, 2
I have read the CLMM package description, and it does not specify what is going on under the hood.

Created using this code:

vegtrans$tsf <- with(vegtrans, factor(tsf, levels=c('S','M','XL'), 
                                    ordered=TRUE)

Best Answer

These aren't separate models for the linear and quadratic term for tsf; the results you show are for one single model containing both terms. What the results are suggesting is that you need to have the quadratic term rather than just represent/approximate tsf as a linear function only.

Related Solutions

Solved – Plot and interpret ordinal logistic regression

My Regression Modeling Strategies course notes has two chapters on ordinal regression that may help. See also this tutorial.

The course notes go into detail about what model assumptions mean, how they are checked, and how to interpret the fitted model.

Mixed Model vs Ordered Probit vs Ordered Logit – Comparing Linear Models with Ordinal Response

This is going to be at best a partial answer but hope it helps a little.

Given that your response is ordinal you have to ask yourself whether the distance between different categories is different depending on the starting position. In other words. If you think the gap between 1 and 3 is not necessarily the same gap as the gap between 2 and 4, then using a cumulative link model (e.g. logit or probit) is the best option. I'd recommend reading the tutorial and extra information from Christensen (2013) on the ordinal package to help you along the way.

Why people prefer lmer() has probably less to do with good statistics or econometrics and more with habit, and method institutionalisation. I know from experience that coming up with a CLM model while most people use a GLS or OLS or so can be ill-advised not because the CLM is not a better model, but because you are basically telling your community of readers "so far you guys were wrong" which is not that easy to swallow.

Centering and standardizing is often done because people think it will alleviate specific concerns of collinearity and so. There is much debate all over the place about whether this is true but in my opinion (and the same goes for log-transformations) you are reducing variance and changing the data which is only a good idea if you have a theoretical motivation for this, if not, work with the actual data and change your model.

As to the choice of logit versus probit. The difference is not that big in general. Once again I would be guided by the data. You can start as follows:

# Finding the best matching link function
links <- c("logit", "probit", "cloglog", "loglog", "cauchit")
sapply(links, function(link){
  clm(formula, data=df, link=link)$logLik})
    # See which one fits best

# Finding the best threshold function
thresholds <- c("symmetric", "flexible", "equidistant")
sapply(thresholds, function(threshold){
  clm(formula, data=df, link="select best fitting link function",threshold=threshold)$logLik
})

This will give you the best fit between your data depending on the model (lowest log-likelihood). In general, the probit is better if you have a lot of "extreme" values (i.e. worst and best in your case) because it is tied to the normal distribution which has fatter tails than the logistic one (logit).

Finally, here is some simple code that will give you a very good idea of how well your model (and X variables) allow you to predict the response variable. This code will plot the incidence of right responses and the number of wrong predictions (and how wrong they are) in your model.

pred. <- predict(FORMULA, type = "class")$fit
    plot(df$RESPONSE,pred.,type="p", pch=15,cex = sqrt(table(df$RESPONSE,pred.))/5)
     # YOU WILL SEE THIS PLOT IS NOT THAT USEFUL
    results <- data.frame(cbind(as.numeric(as.character(df$RESPONSE)),as.numeric(as.character(pred.)),as.numeric(as.character(df$RESPONSE))-as.numeric(as.character(pred.))))
      sum(results[,3]) # THIS WILL GIVE YOU A FAST IDEA ABOUT WHETHER YOU OVERESTIMATE (LARGE POSITIVE VALUE, OR UNDERESTIMATE, THE ACTUAL RESPONSE
      results$dum <- 1
  tmp <- data.frame(with(results, tapply(dum, results[,3],sum)))
  tmp$z <- seq(min(results[,3]),max(results[,3]),by=1) 
      plot(tmp$z,tmp[,1], type="h", xlab ="Deviation from correct prediction",ylab="Number of Predictions")

Let me know what you think!

Simon

Best Answer

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Solved – Plot and interpret ordinal logistic regression

Mixed Model vs Ordered Probit vs Ordered Logit – Comparing Linear Models with Ordinal Response

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