1_ Factor Analysis

8/3/2019 1_ Factor Analysis

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Problem 1: Factor Analysis

Problem 1.1 Modularity Level of NPD Project

In Problem 1.1, we have beliefs about the constructs underlying the Modularity Level questions;

we believe that there are two constructs: Modular Design, and Modular Level.

Modularity Level (ml)

Modular Design

Modular Level

Social Capital (sc)

Social Interaction

Network Position

Project Leadership Style (ls)

Participating Style

Selling Style

Telling Style

Delegating Style

Team Member Diversification (in)

Knowledge Diversification

Social Category Diversification

NPD Performance (npd)

Product Prototype

Development Proficiency

Product Launch Proficiency Technological Core

Competency

Market Forecast Accuracy

Design Change Frequency

Product Development

Cycle Time

Innovation Level


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Analyze => Dimension Reduction => Factor

Next, select the variables ml1 through ml8.

Now click on Descriptives

Then click on the following: Initial solution (under Statistics), KMO and Barletts test of

sphericity (under Correlation Matrix)

Click on Continue


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Next, click on Extraction

Select Principal components from the Methods pull-down Click on Unrotated factor solution (under Display). Also, check the Scree plot box

(under Display)

Click on Continue

Now click on Rotation

Click on Varimax, then make sure Rotated solution is also checked.

Click on Continue


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Next, click on Options

Click on Sorted by size Click on Continue then OK

Output 1.1: Factor Analysis for Modularity Level

FACTOR

/VARIABLES ml1 ml2 ml3 ml4 ml5 ml6 ml7 ml8

/MISSING LISTWISE

/ANALYSIS ml1 ml2 ml3 ml4 ml5 ml6 ml7 ml8

/PRINT INITIAL KMO EXTRACTION ROTATION

/FORMAT SORT

/PLOT EIGEN

/CRITERIA MINEIGEN(1) ITERATE(25)

/EXTRACTION PC

/CRITERIA ITERATE(25)

/ROTATION VARIMAX

/SAVE BART(ALL)

/METHOD=CORRELATION.


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Testsofassumptions.

Shouldbegreaterthan.50indicatingsufficientitemsforeachfactor.Shouldbesignificant(lessthan.05),indicatingthatthecorrelationmatrixissignificantlyfromanidentitymatrix,inwhichcorrelationbetweenvariablesareallzero.

Thesecommunalitiesrepresenttherelationbetweenthevariableandallothervariables(i.e.,thesquaredmultiplecorrelationbetweentheitemandallotheritems).Shouldbebiggerthan.50tobeusedasareference,notasadeletecriteria.

Eigenvaluesrefertothevarianceexplainedoraccountedfor.Percentofvarianceforeachcomponentbeforeandafterrotation.


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The items cluster into these two groups

defined by high loadings.

Thescreeplotshowsthatafterthefirstfivecomponents,increasesintheeigenvaluesdecline,andtheyarelessthan1.0.


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Interpretation of Output 1.1

The factor analysis program generates a number of tables depending on which options have

chosen. The first table in Output 1.1 is the Kaiser-Meyer-Olkin (KMO) measure which tells one

whether or not enough items are predicted by each factor. The KMO test should be greater

than .50. The Barlett test should be significant (i.e., a significance value of less than .05); this

means that the variables are correlated highly enough to provide a reasonable basis for factor

analysis.

Next, the Total Variance Explained table shows how the variance is divided among the 8

possible factors. Note that two factors have eigenvalues (a measure of explained variance)

greater than 1.0, which is a common criterion for a factor to be useful. When the eigenvalue is less

than 1.0, this means that the factor explains less information than a single item would have

explained. The computer has looked for the best two-factor solution by rotating two factors.

For this and all analyses, we will use an orthogonalrotation (varimax). This means that the final

factors will be as uncorrelated as possible with each other. As a result, we can assume that the

information explained by one factor is independent of the information in the other factors. Werotate the factors so that they are easier to interpret. Rotation makes it so that, as much as

possible, different items are explained or predicted by different underlying factors, and each factor

explains more than one item. One thing to look for in the Rotated Matrix of factor loadings is the

extent to which simple structure is achieved.

The Rotated Factor Matrix table, which contains these loadings, is key for understanding the

results of the analysis. Note that the computer has sorted the 8 modularity level of NPD project

(ml1 to ml8) into two overlapping groups of items, each which has a loading of |. 60| or higher |. 60|

means the absolute value, or value without considering the sign, is greater than .60). Actually,

every item has some loading from every factor, but there are blanks in the matrix where weightswere less than |. 60|. Within each factor (to the extent possible), the items are sorted from the one

with the highest factor weight or loading for that factor (i.e., ml4for factor 1, with a loading of .836)

to the one with the lowest loading on that first factor (ml5). Loadings resulting from an orthogonal

rotation are correlation coefficients of each item with the factor, so they range from -1.0 through 0

to +1.0. Usually, factor loadings lower than |. 60| are considered low, which is why we suppressed

loadings less than |. 60|.

Principal axis factor analysis with varimax rotation was conducted to assess the underlying

structure for the eight items of the Modularity Level Questionnaire. Two factors were requested,

based on the fact that the items were designed to index two constructs: modular design, and

modular level. After the rotation, the first factor accounted for 37.5% of the variance, and the

second factor accounted for 65.8%. Table 1.1 display the items and factor loadings for the rotated

factors, with loadings less than .60 omitted to improve clarity.


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Table 1.1Factor Loadings for the Rotated Factors Modularity Level

ItemsFactor Loading

Communality1 2

ml4 Our NPD project use modularized design 0.821 0.681

ml1 Our NPD project share common modules 0.734 0.616

ml2 Our new product features are designed around a standardbase unit 0.732 0.637

ml3 Our new products can be customized by adding featuremodules as requested

0.836 0.698

ml5 Our new product feature modules can be added to astandard base unit

0.677 0.545

ml6 Our new product modules can be rearranged by end-usersto suit their needs

0.837 0.727

ml7 Our new product could partially upgrade, conveniently wearand tear or adapt new components

0.830 0.706

ml8 Our new product modules can be reassembled into

different forms

0.781 0.661

Eigenvalues 3.001 2.270% of variance 37.510 65.889

The first factor, which seems to index competence, loads most strongly on the first five items, with

loadings in the first column. The second factor was, which also seems to index competence

composed of the three items with loadings in column 2 of the table.


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Problem 1.2 Leadership Style of NPD Project

In Problem 1.2, we have beliefs about the constructs underlying the Leadership Style questions;

we believe that there are four constructs: Participating Style, Selling Style, Telling Styleand

Delegating Styles.

Modularity Level (ml)

Modular Design

Modular Level

Social Capital (sc)

Social Interaction

Network Position

Project Leadership Style (ls)

Participating Style

Selling Style

Telling Style

Delegating Style

Team Member Diversification (in)

Knowledge Diversification

Social Category Diversification

NPD Performance (npd)

Product Prototype

Development Proficiency

Product Launch Proficiency

Technological CoreCompetency

Market Forecast Accuracy

Design Change Frequency

Product Development

Cycle Time

Innovation Level


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Analyze => Dimension Reduction => Factor

Next, select the variables ls1 through ls16.


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Now click on Descriptives

Then click on the following: Initial solution (under Statistics), KMO and Barletts test of

sphericity (under Correlation Matrix)

Click on Continue

Next, click on Extraction

Select Principal components from the Methods pull-down

Click on Unrotated factor solution (under Display). Also, check the Scree plot box

(under Display)

Click on Continue

Now click on Rotation Click on Varimax, then make sure Rotated solution is also checked.

Click on Continue


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Next, click on Options

Click on Sorted by size Click on Continue then OK

Output 1.2: Factor Analysis for Leadership Style

FACTOR

/VARIABLES ls1 ls2 ls3 ls4 ls5 ls6 ls7 ls8 ls9 ls10 ls11 ls12 ls13 ls14 ls15 ls16

/MISSING LISTWISE

/ANALYSIS ls1 ls2 ls3 ls4 ls5 ls6 ls7 ls8 ls9 ls10 ls11 ls12 ls13 ls14 ls15 ls16

/PRINT INITIAL KMO EXTRACTION ROTATION

/FORMAT SORT

/PLOT EIGEN

/CRITERIA MINEIGEN(1) ITERATE(25)

/EXTRACTION PC

/CRITERIA ITERATE(25)

/ROTATION VARIMAX

/SAVE BART(ALL)

/METHOD=CORRELATION.


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Testsofassumptions.

Shouldbegreaterthan.50indicatingsufficientitemsforeachfactor.

Shouldbesignificant(lessthan.05),indicatingthatthecorrelationmatrixissignificantlyfromanidentitymatrix,inwhichcorrelationbetweenvariablesareallzero.

Thesecommunalitiesrepresenttherelationbetweenthevariableandallothervariables(i.e.,thesquaredmultiplecorrelationbetweentheitemandallotheritems).Shouldbebiggerthan.50tobeusedasareference,notasadeletecriteria.


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Deleted ls10


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Deleted ls4

Deleted ls8


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Deleted ls16

Deleted ls11


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Deleted ls14

Deleted ls15

Documents

1_ Factor Analysis