Interpreting negative coordinates and origin in 2D correspondence analysis plot

Question

• Why are there negative values in the range of the plot?
• How is the center of the plot (i.e., the $0.0$ point) found?
• How did the black-brown points end up in the third quadrant of the plot?
• Why are red, hazel, & brown positive on the y-axis and negative on the x-axis?

I just really need to learn how to interpret this kind of simple diagram before going further.

_{This picture was taken from another question on Cross Validated.}

Answer 1

• Why are there negative values in the range of the plot? Because the input contingency table of positive values (e.g. frequencies) was standardized by the analysis in a special way relative the central point.
• How is the center of the plot (i.e., the 0.0 point) found? It is the weighted mean row profile and the weighted mean column profile. It is thus the locus of "perfectly typical" or predominant hair and eye colour. According to your data, brown hair and hazel eyes are the closest candidates to be called "typical" of the population.
• How did the black-brown points end up in the third quadrant of the plot? What quadrant - it doesn't matter. Row and column points which are close together tend to co-occure in the population. Blach hair and brown eyes normally go together, as blond hair and blue eyes. Brown hair is also not uncommon with brown eyes; however, brown hair occurs very often in the population so it also is often seen with combination with some other eyes, mostly hazel.
• Why are red, hazel, & brown positive on the y-axis and negative on the x-axis? As said already, positive/negative sign doesn't matter itself. The general moral following from your map is that Dimension X corresponds to blond vs brown/black opposition, and weaker (less discriminative of the population) Dimension Y corresponds to "colourful" vs "plain" opposition. Note that in simple correspondence analysis you are allowed to rotate the axes as you wish if it facilitates interpretation.