Analytical Solutions | |

Using 1010data's g_function, `g_pca(G;S;XX;Z)`, you can create a model
that corresponds to the principal component analysis of one or more variables. However, in order
to determine the loadings/eigenvectors you need to use `param(M;'evecs';J
I)`.

You have completed a principal component analysis using `g_pca(G;S;XX;Z)`.
Now you are interested in determining the loadings, otherwise known as eigenvectors. Using
the `param` function with the value `'evecs'` as the argument
for the `P` parameter, you can calculate the individual elements of each
eigenvector, but you want to create a matrix containing all of the loadings.

<block name="eigenvector_table" model_vars="age,duration,previous,empvarrate,hsng,h_unk,def"> <base table="pub.demo.mleg.uci.bankmarketing"/> <willbe name="yy" value="y='yes'"/> <willbe name="hsng" value="housing='yes'"/> <willbe name="h_unk" value="housing='unknown'"/> <willbe name="def" value="default='yes'"/> <willbe name="model_pca" value="g_pca(;;{@model_vars};'method''corr')"/> <sel value="i_<=csl_len('{@model_vars}')"/> <willbe name="row" value="i_()"/> <for i="1" to="{csl_len('{@model_vars}')}"> <willbe name="evec_{@i}" value="param(model_pca;'evecs';{@i} row)"/> </for> <colord cols="evec_*"/> </block>

The first part of this solution is discussed in the Principal Component Analysis tutorial,
which can be accessed from the Further reading links below. Once you have your model, you
can use the `param` function to determine the weights of the components.
However, with this function you need to calculate each element individually, specifying the
column and element for each eigenvector.

Storing your model variables or column names in a block variable allows you to
systematically calculate all loadings. You can count the number of elements in your block
variable, `model_vars`, using `csl_len(X)`, and therefore
determine the number of variables included in your model. There will only be as many
eigenvectors and elements within as there are variables in your model, therefore, a
selection is performed to limit the number of rows to this number. You then create a column
that denotes the row number.

Using a `<for>` loop, you can create a column for each eigenvector.
`param(M;'evecs';J I)` takes two numbers in the last argument. The first is
`J`, for the `J`^{th} eigenvector, and
`I`, for the `I`^{th} element in the
`J`^{th }eigenvector. Therefore, you can use the current iteration
number, `{@i}`, for `J` and the current row number,
`row`, for `I`.

After a `<colord>` statement, you are left with the matrix containing the
loadings/eigenvectors for the model produced by
`g_pca(G;S;XX;Z)`.

Note: Notice that you can use `evec_*`
instead of writing out each of the column names and it will include any column name that
starts with "evec_".

If you would like to learn more about the functions and operations discussed in this recipe, click on the links below: