Q1. How to make a partition (stratification; classification) for a variable \(x\) ?

(1) If x is categorical, e.g. landuse types, do nothing;

(2) If x is numerical,

(2a) stratification according to some existing commons, e.g. UN standard for the GDP per capita: poor, middle, …; or

(2b) ordered then equally divided 2~7 strata. Use the stratification with bigger \(q\) and interpretable; or

(2c) try different stratifications, use the one with biggest \(q\). The philosophy similar to regression, in which different coefficient values are tried (or by OLS or MLE) and the one maximizing \(R^2\) is used.

Q2. Will stratification vary with variables?

Yes, stratification can vary with variables, just like regression in which coefficient values vary with variables;

Q3. Software reports error or abnormal result

if numerical \(x\) is used, it must be stratified (see **Q1**), no less than 3 sample units are required in each stratum.

Q4. When \(y\) value should be reported?

(1) When measuring SSH of a variable \(y\): \(100q\)% SSH degree, at \(p\) sig. level.

(2) When attributing \(y\) to x: x explains \(100q\)% of \(y\), no need to report \(p\) value.

Q5. Should \(S_{q_i}\) = 1? where \(i\) stands for \(i^th\) variable

No, because of nonlinear coupling between \(y\) and \(x_i\); or interaction between \(x_i\). For example, U shape association between human mortality (\(y\)) and temperature (\(x\)) can be observed, which means that \(S_{q_i}\) = 1.

Q6. Direction of \(q\)?

No directions for nonlinearity, e.g. Kuznets curve; U shape association between human mortality (\(y\)) and temperature (\(x\)). But, you may check linear direction in each of strata.

Q7. Too big sample, say a remote sensing image composed by 1024´1024 pixels

(1) Resampling, 100 sample units in each of strata are usually enough; or

(2) Use R-Geodetector software, which has no limitation for the sample size.