ttdata

Transition function data

Syntax

T = ttdata(tt,z)

T = ttdata(tt,z,UseZeroLevels=tf)

Description

ttdata evaluates the transition function for observations of the threshold variable. To plot transition functions of threshold transitions, use ttplot.

T = ttdata(tt,z) returns transition function data T for the threshold transitions in tt at values of the threshold variable z.

T = ttdata(tt,z,UseZeroLevels=tf) returns transformation function data with all levels set to 0 when tf is true.

Examples

Evaluate Transition Function

Create logistic threshold transitions at levels 0 and 5.

t = [0 5];
tt = threshold(t,Type="logistic");

tt is a threshold object. By default, the rate of each logistic transition function is 1.

Evaluate the transition function at a sequence of transition variable data from -10 to 10.

z = -10:0.01:10;
F = ttdata(tt,z);
size(F)

ans = 1×2

        2001           2

F is a 2001-by-2 vector of transition function data. Each column is the transition function data for the corresponding threshold in tt.Levels.

Plot Transition Functions at Respective Levels

To facilitate comparisons among transition rates, the Type="graph" option of ttplot graphs all transition functions at the same level. This example shows how to graph transition functions each at their respective level.

Create normal threshold transitions at levels 0 and 5 with rates 0.5 and 1.5, respectively.

tt = threshold([0 5],Type="normal",Rates=[0.5 1.5]);

Evaluate the transition functions at their respective level (the default), and then evaluate them each relative to level 0. Specify a sequence of transition variable data from -10 to 10.

z = -10:0.01:10;  
n = numel(z);

T0 = ttdata(tt,z);
T1 = ttdata(tt,z,UseZeroLevels=true);

T0 is an n-by-1 vector of raw transition function data evaluated at the grid of transition variable data. T1 is an n-by-1 vector of transition function data translated to be centered at level 0.

Plot both sets of transition functions separately.

% Raw transition functions
figure
plot(z,T0,LineWidth=2)
xline(tt.Levels,'--')
grid on
xlabel("Level")
legend(["Level 0, Rate 0.5" "Level 5, Rate 1.5"],Location="northwest")

% Shifted transition functions
figure
plot(z,T1,LineWidth=2)
grid on
xlabel("Distance from Level")
legend(["Level 0, Rate 0.5" "Level 5, Rate 1.5"],Location="northwest")

Input Arguments

tt — Threshold transitions

threshold object

Threshold transitions, with NumStates states, specified as a threshold object. tt must be fully specified (no NaN entries).

z — Threshold variable data

numeric vector

Threshold variable data, specified as a numeric vector.

Data Types: double

tf — Flag indicating whether to compute data with all levels set to zero

false (default) | true

Flag indicating whether to compute data with all levels set to 0, specified as a value in this table:

Value	Description
true	Computes transformation function data with all levels set to 0. This setting is useful for comparing transition rates.
false	Computes raw transformation function data.

Example: UseZeroLevels=true

Data Types: logical

Output Arguments

T — Transition function data

numeric matrix

Transition function data F(z,tt.Levels,tt.Rates), returned as a numeric matrix. F is specified by tt.TransitionFunctionData.

Data in T gives transition function values relative to each level in tt.Levels. The number of rows of T is equal to the length of z and the number of columns is equal to the number of levels. For details, see threshold.

Version History

Introduced in R2021b