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Structural Relationship between LIF and PDI Estimation of PDI using LIF

LIF contains several quantifiable indicators which are
compartmentalized into 9 themes. The value of these indicators
is fed into a statistical model framework to arrive at the
Thematic score and then estimate the value of single PDI by
averaging the thematic score. In other words, it can be said that
the value of indicators from LIF are the inputs to generate the
PDI as output.

In statistical terms, it may be written as:
………………………(1)

Where PDI = which is the mean of thematic scores, where Theme is T, and number of

Themes is i, and i=1(1) 9;
th
Where T i= is the thematic score for i theme which is the mean of indicators under
th
theme i, i=1(1) 9; where I is the Indicator, Ii is the Indicator under Theme i, and j is the j Indicator,
th th
I ij is the j indicator under i theme, j=1(1)n i;
th
n i is the number of indicators in i theme
…………………………………….(1a)

In the above equation 1a, LIF replaced the set of indicators (I). Each of the single indicators combined to con-
stitute a theme and similarly all 9 themes cumulatively create the whole LIF. Hence, an indicator can be con-
sidered as the key elements of LIF and thus LIF is the universal set of the indicators. We can write the same in
a matrix (9 x n i) format:

LIF= =

U ij stands for union of indicators.
Although it is neither conceptually nor statistically justifiable to average indicators’ values within or across
different themes (e.g., birth rate in a GP and bank accounts in the GP, or water bodies and Computer Service
Centre, in the same GP) as the indicators have different units and dimensions, however, to arrive at a holistic
developmental estimate to ensure comparability of PDI with other global and national level indices, the said
method can only be adopted by removing the units from the indicators and making them dimensionless in the
form of percentage, or as binaries.

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PDI Committee Report - 2023: Panchayat Development Index 62