Metodi Quantitativi per Economia, Finanza e Management Lezione n°9
Metodi Quantitativi per Economia, Finanza e Management Lezione n°9
I problemi di una analisi di questo tipo sono:
a)-quante componenti considerare
rapporto tra numero di componenti e variabili;
percentuale di varianza spiegata;
le comunalità
lo scree plot;
interpretabilità delle componenti e loro rilevanza nella esecuzione dell’analisi successive
b)-come interpretarle
correlazioni tra componenti principali e variabili originarie
rotazione delle componenti
Analisi fattoriale
Analisi Fattoriale Sono stati individuati 20 attributi caratterizzanti il prodotto-biscotto
È stato chiesto all’intervistato di esprimere un giudizio in merito all’importanza che ogni attributo esercita nell’atto di acquisto
Qualità degli ingredienti
Genuinità
Leggerezza
Sapore/Gusto
Caratteristiche Nutrizionali
Attenzione a Bisogni Specifici
Lievitazione Naturale
Produzione Artigianale
Forma/Stampo
Richiamo alla Tradizione
Grandezza della Confezione (Peso Netto)
Funzionalità della Confezione
Estetica della Confezione
Scadenza
Nome del Biscotto
Pubblicità e Comunicazione
Promozione e Offerte Speciali
Consigli per l’Utilizzo
Prezzo
Notorietà della Marca
Analisi fattoriale
1. The ratio between the number of components and the variables:
One out of Three
20 original variables
6-7 Factors
2. The percentage of the explained variance:
Between 60%-75%
Factor Analysis 3. The scree plot :
The point at which the scree begins
4. Eigenvalue:
Eigenvalues>1
Factor Analysis
Analisi Fattoriale
5. Communalities:
The quote of explained variability for each input variable must be satisfactory
In the example the overall explained variability (which represents the mean value) is 0.61057
6. Interpretation: Component Matrix (factor loadings)
The most relevant output of a factorial analysis is the so called “component matrix”, which shows the correlations between the original input variables and the obtained components (factor loadings)
Each variable is associated specifically to the factors (components) with which there is the highest correlation
The interpretation of the each factor has to be guided considering the variables with the highest correlations related to single factor Factor Analysis
6. Interpretation:
Correlation between
Input Vars
&
Factors
The new Factors must have a meaning based on the correlation structure
6. Interpretation:
The correlation structure between
Input Vars
&
Factors
In this case the correlation structure is well defined and the interpretation phase is easier
Issues of the Factor Analysis are the following:
a) How many Factors (or components) need to be considered
6. The degree of the interpretation of the components and how they affect the next analyses
b) How to interpret
The correlation between the principal components and the original variables
The rotation of the principal components
Factor Analysis
6. Interpretation: The rotation of factors
There are numerous outputs of factorial analysis which can be produced through the same input data
These numerous outputs don’t provide interpretation that are remarkably different from one another, as matter of fact they differ only slightly and there are areas of ambiguity Factor Analysis
x3 x4 CFi CFj x1 x2 The coordinates of the graph
are the factor loadings Interpretation of the
factors CF*i CF*j Factor Analysis
6. Interpretation: The rotation of factors
The Varimax method of rotation, suggested by Kaiser, has the purpose of minimizing the number of variables with high saturations (correlations) for each factor
The Quartimax method attempts to minimize the number of factors tightly correlated to each variable
The Equimax method is a cross between the Varimax and the Quartimax
The percentage of the overall variance of the rotated factors doesn’t change, whereas the percentage of the variance explained by each factors shifts Factor Analysis
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