Competency 6.2: Key Diagnostic Metrics

A part of Week 6 was designed to learn about the diagnostic metrics, to see how well our model does, as either classifiers or regressors. 

Metrics for Classifiers


The easiest measure of model goodness is accuracy. It is also called agreement, when measuring the inter-rater reliability.

Accuracy = # of agreements/ Total # of assessments

It is generally not considered a good metric across fields, since it has non even assignment to categories and not useful. E.g. 92% accuracy in the Kindergarten Failure Detector Model in the extreme case always says Pass.


Kappa = (Agreement – Expected Agreement) / (1 – Expected Agreement)

If Kappa value
= 0, agreement is at chance
= 1, agreement is perfect
= negative infinity, agreement is perfectly inverse
> 1, something is wrong
< 0, agreement is worse than chance
0<Kappa<1, no absolute standard. For data-mined models, 0.3-0.5 is considered good enough for publishing.
Kappa is scaled by the proportion of each category, influenced by the data set. We can compare the Kappa values within the same data set, but not between two data sets.


The Receiver Operating Characteristic Curve (ROC) is used while a model predicts something having two values (E.g correct/incorrect, dropout/not dropout) and outputs a probability or other real value (E.g. Student will drop out with 73% probability). 

It takes any number as cut-off (threshold) and some number of predictions (maybe 0) may then be classified as 1’s and the rest may be classified as 0s. There are four possibilities for a classification threshold:
True Positive (TP) – Model and the Data say 1
False Positive (FP) – Data says 0, Model says 1
True Negative (TN) – Model and the Data say 0
False Negative (FN) – Data says 1, Model says 0

The ROC Curve has in its X axis Percent False Positives (Vs. True Negatives) and in Y axis Percent True Positives (Vs. False Negatives). The model is good if it is above the chance line in its diagonal.


A’ is the probability that if the model is given an example from each category, it will accurately identify which is which. It is a close relative of ROC and mathematically equivalent to Wilcoxon statistic. It gives useful result, since we can compute statistical tests for:
– whether two A’ values are significantly different in the same or different data sets.
– whether an A’ value is significantly different than choice.

A’ Vs Kappa:

A’ is more difficult to compute and works only for 2 categories. It’s meaning is invariant across data sets i.e) A’=0.6 is always better than A’=0.5. It is easy to interpret statistically and has value almost always higher than Kappa values. It also takes confidence into account.

Precision and Recall:

Precision is the probability that a data point classified as true is actually true.
Precision = TP / (TP+FP)
Recall is the probability that a data point that is actually true is classified as true.
Recall = TP / (TP+FN)
They don’t take confidence into account.

Metrics for Regressors

Linear Correlation (Pearson correlation):

In r(A,B) when A’s value changes, does B change in the same direction?
It assumes a linear relationship.
If correlation value is
1.0 : perfect
0.0 : none
-1.0 : perfectly negatively correlated
In between 0 and 1 : Depends on the field
0.3 is good enough in education since a lot of factors contribute to just any dependent measure.
Different functions (outliers) may also have the same correlation.

R square:

R square is correlation squared. It is the measure of what percentage of variance in dependent dependent measure is explained by a model. If predicting A with B,C,D,E, it is often used as the measure of model goodness rather than r.


Mean Absolute Error/ Deviation is the average of absolute value of actual value minus predicted value. i.e) the average of each data point’s difference between actual and predicted value. It tells the average amount to which the predictions deviate from the actual value and is very interpret able.


Root Mean Square Error (RMSE) is the square root of average of (actual value minus predicted value)^2. It can be interpreted similar to MAD but it penalizes large deviation more than small deviation. It is largely preferred to MAD. Low RMSE is good.

Goes in the right direction, but systematically biased
Values are in the right range, but doesn’t capture relative change

Information Criteria:


Bayesian Information Criterion (BiC) makes trade-off between goodness of fit and flexibility of fit (number of parameters). The formula for linear regression:
BiC’ = n log (1-r^2) + p log n 
where n – number of students, p – number of variables
If value > 0, worse than expected, given number of variables
   value <0, better than expected, given number of variables
It can be used to understand the significance of difference between models. (E.g. 6 implies statistically significant difference)


An Information Criterion/ Akaike’s Information Criterion (AiC) is an alternative to BiC. It has slightly different trade-off between goodness and flexibility of fit.

Note: There is no single measure to choose between classifiers. We have to understand multiple dimensions and use multiple metrics.

Types of Validity


Does your model remain predictive when used in a new data set?
Generalizability underlies the cross-validation paradigm that is common in data mining. Knowing the context of the model where it will be used in, drives the kind of generalization to be studied.
Fail: Model of boredom built on data from 3 students fails when applied to new students

Ecological Validity:

Do your findings apply to real-life situations outside of research settings?
E.g. If a behavior detector built in lab settings work in real classrooms.

Construct Validity:

Does your model actually measure what it was intended to measure?
Does your model fir the training data? (provided the training data is correct)

Predictive Validity:

Does your model predict not just the present, but the future as well?

Substantive Validity:

Does your results matter?

Content Validity:

From testing; Does your test cover the full domain it is meant to cover?
For behavior modeling, does the model cover the full range of behavior it is intended to?

Conclusion Validity:

Are your conclusions justified based on evidence?

I think that the lessons in Week 5 and 6 are very useful, especially when we want to get our hands deep into predictive modeling and diagnosing its usefulness. I hope to use them in my predictive modeling work 🙂

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