Joinpoint regression

Joinpoint regression fits straight segments through a trend over time and finds the years where the direction or steepness changes. This article runs it on the Overdose death rate (per 100,000) for the 88 Ohio counties in the Ohio overdose trends sample, 2003 to 2021, as one statewide series. Every step below was run on Vesta Online, and the screenshots come from that run. For a shorter first run with the defaults, see the Quickstart.

The six steps

1. 1Open a project that holds your dataOpen the Projects page, select a project and choose Open Project. This walk-through uses a copy of the Ohio overdose trends sample, whose Ohio counties dataset has 88 objects and 19 time periods.
2. 2Choose Joinpoint regressionChoose Analyze, then Detect a trend over time, then Joinpoint regression, and choose Pick a method. The analysis has five steps: Analysis, Variables, Model, Run and Summary.
3. 3Pick the variableOn Variables choose the dataset, Ohio counties, and the variable, Overdose death rate (per 100,000). It is one measure at a time, and a binary variable is not offered. An object with no valid observation at two distinct times is left out of the fit, not treated as zero. The side card shows the Most joinpoints the timeline supports; here it is 3, so the run fits 4 candidate models: no joinpoint, then one per number of segments this timeline supports. It keeps the one with the lowest BIC. Choose Next: Model.
4. 4Set the modelModel sets the scale, the series and the errors. Leave the scale on Log-Linear, the default, so the trend reads as an annual percent change. Under Group data by choose Combine all, one series over everything; the default, Separate by ID, fits one series per object. Under Errors choose Heteroscedastic and pick Death rate standard deviation, so a noisy year pulls the line less; the default, Homoscedastic, treats every observation as equally precise. The card on the right repeats what the run will fit. Choose Run analysis.
5. 5Run the analysisThe run happens on the server. If you start a second run while another of yours is going, the step says Another analysis of yours is still running. The Summary then lists what was saved and what to check.
6. 6Open the result workspaceChoose Open in workspace. The result workspace has the Joinpoint Regression Summary, a plot of the data and the fitted trend, two maps and a statistics panel.

What you should see

The method

Analysis

Detect a trend over time lists Joinpoint regression.

The variable

Variables

One dataset and one variable. The side card counts the objects and time periods and the most joinpoints the run can fit.

The model

Model

The card on the right repeats the choices: Log-Linear, all objects in one series, Heteroscedastic, no forecast.

The summary

Summary

The run saved a report, a written summary and ten variables, and says what to check.

The run adds ten variables to the Ohio counties dataset: the estimated mean for each of 0, 1, 2 and 3 joinpoints, the years of the first, second and third joinpoint in the most parsimonious model, the most parsimonious model itself, its estimated mean and its AAPC. The Most Parsimonious Estimated Mean is what the chosen model fits at each location, and the Most Parsimonious AAPC is its average annual percent change: positive is rising, negative falling. A group with fewer joinpoints leaves the later joinpoint years missing, not zero.

The result

Result workspace

The summary table, the plot, the Best AAPC map (6.79 in every county) and the Most Parsimonious Estimated Mean map.

Reading the result

The run fitted four models to the statewide series. The one with the lowest BIC is the most parsimonious, and the summary highlights its row:

Joinpoints	BIC	Segments	APC (%)	AAPC (%)
0	4.1168	2003 to 2021	6.54	6.54
1 (chosen)	4.0742	2003 to 2014; 2014 to 2021	4.44; 10.59	6.79
2	4.0748	2003 to 2006; 2006 to 2013; 2013 to 2021	9.40; 2.83; 10.38	7.22
3	4.0807	2003 to 2006; 2006 to 2012; 2012 to 2018; 2018 to 2021	9.59; 2.57; 8.43; 13.72	7.48

The chosen model has one joinpoint, in 2014. The death rate rose about 4.4 percent a year from 2003 to 2014 and about 10.6 percent a year from 2014 to 2021, and the average annual percent change over the whole period is 6.79 percent. The BIC of the one-joinpoint model (4.0742) and the two-joinpoint model (4.0748) are very close, so the data barely separate them; read the segments beside the joinpoint rather than quoting one number. A joinpoint is where the fitted slope changes, not where the series peaks.

Because the run used Combine all, there is one group, so every county carries the same value in both result maps. The Best AAPC map is one orange, and its legend shows the one value, 6.79, for 88 counties, plus a Missing row at 0; a map of one value shows no pattern across the state.

Watch outThe log-linear model drops every observation at or below zero before fitting, because they cannot be logged, and it gives no error. The trend is then fitted on fewer points than the data has. The linear model keeps them.

Watch outHeteroscedastic errors weight each observation by its standard deviation. An observation whose standard deviation is missing or zero is weighted as if it were certain, so check that column before you rely on this model.

NoteThis walk-through used Log-Linear, Combine all, Heteroscedastic errors and no forecast. Linear, Separate by ID, grouping by a categorical or binary column, Predict forward and the compositional option were not run for it, so the screenshots do not show them. Predict forward is a percentage of the observed timeline from 0 to 100 (the default is 0), and a forecast adds valid times to the layer itself, so every other view of it shows the extended period. Compositional analysis, which fits the parts of a whole together, shows the Whole and its Parts instead of one variable and draws no maps.

NoteJoinpoint regression needs more than one time period in the dataset, and at least six periods before it can place a joinpoint, because each segment needs 3 observations. A shorter series produces only the straight line, with its estimated mean and average annual percent change, and no change year.

Where next

• Your first run, with the defaults: Quickstart.
• Another way to see where values cluster: Local cluster analysis.
• Bring in your own data: Importing data.

Not sure which method fits your question? When the Advisor is turned on, you can describe your question on the Analysis step and let the Advisor suggest one. The Advisor is an optional AI-assisted guided workflow; see Using the Advisor.