Good morning everyone, welcome to the class
of marketing research and analysis. Till now, we have covered different aspects of marketing
research, the different tools which are utilized in conducting a marketing research study well this
studies might not be these tools and techniques need not to be used for marketing research, they
can be largely utilized for other research propose also right. Today, what we are going to cover
is another very important technique which is basically called as interdependence techniques.
So, it is called as a interdependence technique okay, now why it is called interdependence
techniques basically the reason being very simple that in this case we do not have any
dependent or independent variable right we do not have dependent or independent variable
okay, so, what is the use of this technique, why do we use it first of all, and where it is
used let me tell you this technique that I am going to describe or explain is one such technique
which has been which is largely utilized heavily utilized and sometimes it is, I can also say
miss utilized people use researchers use it for different purposes without understanding the
very basic reason of they are doing it right.
So, what is the static if we are taking
about this technique? is basically utilized to you know bring down large amount of data
sets to a fewer meaningful once right that means what I am try to say, for example,
let us say a company wants to know how, do people by a certain product or what variables
impact the you know the customers right?
So, suppose it has taken 100 variables let
us assume right 100 variables now trying to analysis 100 variables and coming out with
the meaningful you know explanation is a tough job because it is too tough to analysis
100 variables across may be 500 or 1000 participants or 10000 participants whatever it
is right, so in such a case, we need to have technique which can bring down this data
to a fewer once to a very less number.
So that, that become simpler for the researcher
to analyze and interpret and understand interpret that okay so this technique that we are talking
about is basically called the factor analysis okay so factor analysis is nothing but a
data summarization and a data reduction technique right, it basically helps you in data
summarizing the data and reducing the data okay, so let us see the factor analysis.
So, it says it basically examines the interrelationships among a large number
of variables as I said right there are 100 variables and you need to find out some
meaningful you know meaningful meaning out of it so in such a condition if this 100 could be
reduced to let us say only 6 or 7 or 10 maximum then we would assume okay it is much simpler
to explain this 10 rather than the 100 okay.
So what it does is basically it attempts to
explain this 100 variables on basis of some common underlying dimension now what is this
common underlying dimension you can understand is like some similarity some you know groups that
could be formed right for example let us say there are the you know students who are who can be you
know good in studies, who can be good in sports, who can be good in let us say culture.
Cultural activities so now everything that is related to somewhat related to even culture
would be brought under one group that is called culture right and everything the students
does basically may be his GP is scores CGPA or his some other examination score or something
right. All these could be brought under another category called let us say academics okay and
similarly suppose he as done anything in sports, in yoga in anything right relative health
and mental health and spiritual health.
So, in that we would say this can be brought
under the category of let us say the sports okay so making those bring in those let us say large
number of variables to 3 now form example is what is the bases of intention of factor analysis.
As I said it is a interdependent technique and there are no independent or dependent variables
Earlier when we did regression analysis we said it is a causal model it is a cause and effect there
is causal right, so in that we had a Y and X, Y was the dependent and X was the independent
variable so we said the whatever the change in Y will happen is because of the change in X okay so
that was something which was related there was a relation between the two variables but here we are
not doing anything of that kind we are not doing any relationship of dependent and independent.
However, let me add to the you know understanding of the listener out here that the interpretations
or the, the results that you derive from factor analysis can add the end maybe or can be utilized
as a dependent and independent variable later on that means you can create dependent variables
independent variable out of these out of this data summarization okay, I will explain
that later so what it is saying is.
Determines a small number of factors based on a
particular number of inter related quantitative variables so first of all please remember when
you conduct a factor analysis factor analysis is to bring down all the variables together
so that they can be you know some meaningful pattern can be brought out of it, here we
are not taking any string variables or non quantitative variables right we even would like
to avoid, we are not doing any non metric right variables or let say categorical nominal data.
All kind of variables right suppose you are not interested in taking any demographic variables
as such we are not interested because if you want to take a something if you want to do a
factor analysis, factor is basically will be done and on continuous data that is data which
is collected on a maybe an interval scale okay, interval scale so this is one thing another thing
is that if you want if you want to do a factor analysis on let say a non-metric data for that
you have something called a Boolean algebra.
Or Boolean factor analysis which is not the part
of our course and we are not doing it, so what is it saying basically so interrelated quantity
variables first thing right, second it says if you see in social science what happens is to
measure a particular you know particular concept let say we cannot many a times we are not able
to measure it directly right, so what we do we measure it through indirectly through some other
ways for example if I am interested in measuring let say honesty, honesty I may not be able to
measure a honesty through a single item right because it is a it is kind of an abstract thought
right, so in order to understand better what we do is we ask certain number of questions.
Or items to which are concerned about honesty okay, so third thing they are saying is they
construct that are derived from the measurement of other directly observable variables that
means what are those observable variables now suppose in your question here suppose you
have framed a survey instrument a question at in which you had 1 2 3 4 let say 10 questions
okay, and this was related to honesty this was related to honesty this was related to
trust this was related to satisfaction.
Maybe this was related to again honesty
right this was related to satisfaction. So, now this this this, these three are actually a
observable variables which are somewhere related to honesty that is why I have given the name
honesty and when we bring this three together they come under the group honesty okay. So, why is
it required for a marketer? A marketer is requires it very largely because when we do the initially
the study we take large number of variables in order to understand the respondents psychological
profile but somewhere what so what happens is that in the context of doing the research we
have taken large amount of variables and at the end we feel okay we have taken too much.
And by taking too much we are unable to actually deduce a or come to a proper inference okay what
is a assumptions you have in factor analysis.
Basically the variables must be related
that means what when you take when you take when you conduct a factor analysis there
is assumption that the items within the factor there has to be some degree of correlation
right there should be sufficient number of.
Sufficient number of correlations there is a
even a test for which we do the Bartlett test of sphericity which we will test, we will test
to we want it to be significant we will see that when I show you and most of the factor analysis
studies when you see some software you know output also you see that Bartlett test it says if it is
significant that means there is some correlation among the variables that is the meaning of
it, right. The variables are assumed to be metric as I said multivariate normality is
not a condition that is important, right.
If it is not there it does not make of much of
a difference in your study right, now what is the sample size to conduct a factor analysis the
sample size should be around 100 at least right, although 50 is there but 50 is a very small
number right, that is the minimum amount but if you have anything less than 100 it is so wise
to conduct a factor analysis and if you have anything above 100 it is a ideal number, right.
How I think I have explained okay, what should be the criteria of understanding the number of
respondents or number of cases it is one variable or one item that you have taken in the study
multiplied with an average of 10 respondents, so if you have 20 variables in your study that
means your average should be respondents size should be at least 200, right. So minimum it
says is 5 that is basically in a BtoB sector where data is very difficult to obtain, so 5
is the minimum and maximum is up to 20 we say, 20 is the very ideal number so if you have 20
variables 400 that means, okay. But in between is 10 right, now what is the purpose as I said?
It is a data reduction technique right, so its objective is to simplify the items into subsets of
concepts or measures right, so it simplifies into creating subsets okay. It helps in validating the
construct, the construct is the factor honesty, for example there, right, so it helps to even
validate so we will check how validation is also done with through discriminate validity
convergent validity basically construct validity, there is a process, right. So, issues, now
what the two methods basically students are always they are interested to know okay.
What is the method? Very famously we have the principle component analysis, now what
is this principle component analysis right, and against what I am talking about the two
techniques which are used to derive factors in a study so one is the principle component
analysis, the other being the common factor analysis, right common factor analysis or just
factor analysis also people say that, right.
Now, what is this difference between the
principle component and the common factor, the difference between the principle component
and the common factor being one the point is here the total variance is taken into account to
derive the factors, right so all the complete all variance is taken where basically we talk about
complete variance means the unique variance right, and the you know the error variance right, so
we have unique variance specific variance and error variance, share variance basically.
The unique specific or shared variance right, or common variance shared or common right, so
these three variances together make the 100%, so in during the principle component
analysis there is no difference, they do not create any difference between the
three and the total variance is taken into whole, but in the common factor analysis only
those variance, those data are taken which share this common the variance commonly.
So, like if you look at like a Venn s diagram so suppose this is the common area right, so this
is the common variance so in a common factor analysis we talk about this variance right, and
we are less bothered about the others, right. But there is a problem with you know the most utilized
is the principle component analysis and we highly seldom talk about the you know common factor very
less, principle component is mostly utilized.
So, the question is how many factors are the
right, you know how many should the researcher derive suppose your 100 variables so how many
factors should I derive out of this 100 variables 5,7,10 how many what is the right number we
do not know, then comes a question when you create the factor right, sometimes what happens
there are terms which I will be used slowly the factors sometimes you know the variables are
loaded in to only one factor many a times that means when you create a factor analysis right.
You will see that most of the factors they are loaded most of the variables not factor variable
are loaded on to the first factor. Now what does it mean now suppose let us say like this suppose
I have ten factors ten variable sorry v3 v4 v5 v10 okay this is factor 1 factor 2 factor
3 okay three factors are there it might be possible that was the first six variable are
loaded in to the first factor only right.
And only two of this are only one is loaded in
to the second factor and two again the third factor so because of this kind of problems what
happens although if we are purpose is only data redaction then no issues right but suppose you
want to have a better pattern because it is so happens that it looks very strange that six
variables are loaded in to the first factor and the other are not getting sometime it might
not be even two only one so it looks very odd in those case what we do is we use something called
a factor rotation so why by rotating the factor the distribution of the variables is made much
better across the factor okay we will see that.
And finally how to interpret now the tool one
thing is very important to understand loadings, now what is a loading? Loading is basically
every variable loads in to the factor it has certain value let us say 0.7 let us say 0.65
okay 0.84 now what does it mean? It means that in simple terms if you want to understand that
these loadings are nothing but the correlation of the variable with the factor.
So, you will see that sometimes this is 0.7 this could be maybe 0.12 this could be the
remaining or something like this right let us say 0.18 okay. Now similarly what happen is that
means if a variable is loaded very high on to one factor it generally should be loaded less
in to the other factors okay that means it is very unique thing it is only for this factor it
should not spreading across to other factors.
But we do face a problem in certain cases what are
the problems, the problems are that sometimes we see that some variables show a high correlation
between two factors factor one and factor two factor one and factor three factor two and factor
three so this is something a problem right this problem is called a problem of cross loading
now what should you do? So what should you do in this cross loading we will we see that.
So, if you look at now the as I said I started with I did not say one thing that factor
analysis when I say there are two types of factor analysis the first is call the EFA
and then there is another one called CFA right EFA being the exploratory factor analysis
as a name suggested you are exploring so you are exploring the variables to come
out with certain number of factors that you are not knowing at the beginning.
So, after the study you after conducting the exploratory factor analysis you can come to
you can get knowledge well, five or six factors are coming maybe out of this 100 variables
or ten right whatever. But in the case of it confirmatory factor that is a different story
where already there is a theory behind it and already the factors you are only conforming the
whether the factors are ideally or adequately explaining the you know the research study or
not that means what in such cases the researcher already knows what are the factors and how they
are related he is only going to test them okay, cross checking basically you can say.
So, what it does basically principle component analysis explains consider the
total variance and derives factors contain little amount of unique and error variance.
So, it is takes the total variance right and often you within physical science on the other
hand the factor analysis of the common factor analysis considers only the common or shared
variance which I have drawn there right.
And ignores the unique and the error variance
right unique or specific variance what we say it is complicated and thus less utilized that
is why most of the time in the anybody ask you, you can always know you can always
say what is the principle component analysis the principle component analysis
covers the total entire variance and the common factor release on the other hand
only takes the shared variance okay. So, identify the share variance when there is large
number of data pool/ set is difficult right.
So, that is why it is and the beauty is both
factor and both the you know principle component and the common factor analysis give us a similar
result once you are if you see once you have the when the number of variables or the items in your
case or greater than 30 right if your number of items that you are studying is more than 30
then the result that you drive from principle component analysis and a factor analysis common
factor analysis is more or less the same right.
And one more thing if you have a communality I
will explain what is communality, communality is nothing but the shared variances the shared
variance basically the shared variance that means communality is the variable contribution
to each you know factor right so the square of this value the sum of the square of this
value is here is called communality okay.
So, this communality if it is above .60 that
means in almost all the cases if it is .6 then EFA& EFA does not make a difference okay and
as I said conformity factor analysis is used to test whether data fit a priori expectations
right that means already the researcher has in mind a particular theory for example if he is
let say two construct a and b a and b have let say there are three variables V1 V2 V3 V4 V5 V6
right. So, if we there is a clear cut relationship which they are understanding right.
So and this is a covariance model so if, if they know already then it is a case of
a confirmatory but suppose they would not have known then how it would have been it would
have been something like this so all variables running into all other variables right so when
you have all variables running into each other that is exploration case you do not know.
That is why exploring in other cases the confirmatory okay. The basic logic. it says
when you it creates a mathematical combination of variables that maximize the variance,
variance means as I explained earlier the variance is explains the, the explained variance
basically we were talking about whenever we say variance in this case we talking about explained
variance in regression also if you remember.
We had talked about explained and unexplained
variance right so more they explain variance the better there is researcher has conducted
his study right his explanation is better. So, creates new mathematical combination
variables that maximize the variances you can predict in all variables right.
A new combination of an items from residual variance that maximizes the variance and what
is the means what in the first once it derives the first factor let say first factor will
explain the highest amount of variance right let say the overall variance explained is
.7 then the first factor out of it may be explains 30 right and the residual 40 is divided
among the other factors the second factor have explains the second highest variance.
The third factor explains the third highest variance goes on right continue until all
variance is accounted for right all variances that explained variances select the minimum
number of factors that captures the most amount of variance interpret the factors right so once
you have got this factors right now the researcher needs to give a name to this factors.
Now, how will you give a name on what basis will you give a name the name will be given
on basis of the similarity of the variables as I had said that time in the beginning the
all the traits that are related with academia would be clubbed into the group of academics,
all the traits are related to sports will be group under sports and the remaining right.
So this is basically what it has then interpret the factors, once you interpret the factors then
some times as I said , now you have to rotate the factors, now rotating the factors I will explain
again, there are two things, this is how it looks like. So, understand it is like a car, it is
like a car steering right, you are holding the staring, so if you can turn the axis.
So, if I turn the axis let say, so this comes here and this automatically come here,
perpendicularly through an orthogonal rotation or it might not be perpendicular which is called
Oblique rotation. So if I rotate what is happening the variables will be better distributed,
let say variables are like this right, so these variables distribution would be done in the
better way and instead of falling into one factor only which happens usually in the unrotated factor
analysis that will be distributed better okay.
So, few things concept terms that you have
to understand, so what is the factor it is the linear composite of the variables
right, so you multiplied with the weight, weight x independent variable, w1, x1 + w2x2 goes
on all the variables together and factors score.
What is that person s opinion or the score on
the given factor, what is the value or what is his score that is given to the particular
variable is called the factors score. Factors score are utilized heavily at the end of
the study which I tell you to utilized, these factors score can be utilized as the
dependent variable is or independent variable or a regression study, we will see that. Factors
loading I have already explained right communality I have explained. What is the factorally pure?
Sometimes it test only loads only on one factor, so that means we have only single factor, it
is good in some cases that means the no other factors do not. So, there is something called
another term which is important for researcher to understand that is called scale score.
Now, what is the scale score? A scale score is basically nothing but it is the summated scale
score, there are two scores that you can use.
One is the factor score, the factor score
which comes explanation which tells you about, a person, a responded or a case you know, how
much values put on to the particular factor or how much importance, similarly we have something
called the summated scale. Now summated scale is being largely utilized and it is the new
development which is largely used.
Now what is summated scale now let us say
there is a factor 1 okay so factor 1 was nothing but combination of factor v1+v2+v3 let
us say v4, now summated scale says, suppose, this is respondent 1 respondent 2 it goes
on right so whatever score he has given for variable let us say in the scale of 1 to 7 may be
right he has given 5 for this he has given let us say 3 for this he has given let us say 4 for
this he has given again let us say 4 right.
So, the summated value will be nothing but
the average so 5,3,8,4,12 it is divided by 4 so that is 4 for this respondent similarly
for respondent 2 for respondent n 100, 200, whatever so you this summated scale is highly
utilized is a very important tool because later on you can use those factors as an independent
variable or the dependent variable for a different kind of study for a cause effect study right so
that is where it comes off great use right one more thing is when I am saying factor score I
have submitted scale I have explain then there is also something called I Eigen value.
Now what is an Eigen value this is also very important for you to understand now as I said
I explain the communality right I explain the communality there is something also called an
Eigen value now Eigen value is a vertical score right so it is the how you know variables are
loading into particular factor so this squared the sum of the squared loadings across the factor
this total is called the Eigen value right so the Eigen value is one of the ways which is used
to extract factors right in a factor analysis study so Eigen values if it is ;less than 1 we
generally omit right we avoid any factor analysis study which obtains the Eigen value of less
than 1 because that means it is not explaining the item is not explaining itself right.
So, as good as that so Eigen value above 1 is at least that means that the variables or factor
is explaining itself as good as that okay so we will see how many factors how do you interpret
how does the researcher understand, how many factors to be taken right okay what I will do is
we will just I will tell you brief you about the way of identifying the factors which I were just
saying one of the method is through a graphical method which is called as Scree plot method right
like there is a twist you know the bend in the arm so what is the Scree plot I will just show you a
scree plot is basically nothing but you know
This is how the data point changes for example
let say it is something like suppose this is the data point so this is first, second curve, third
curve, fourth then it is stagnant may be so when you see such you know such kind of the arrangement
of data then we say well there are four curvature four points where there are curves the curve is
bending right so we will say there are 4 factors so out of all the variables V1 to Vn. So, we are
saying there are 4 factors coming out so this is the method which is used graphically called
Scree plot test okay. The second is through the latent in root criterion Eigen values
or latent roots if you see you would not get confused is the same thing right so it says
Eigen value greater 1 is used I have just explained y1 right that means it explains
itself at least so Eigen value is greater than 1 is taken as a criteria to generate
the number of factors so one is the amount of variances accounted for by a single item
one is the amount of variance accounted for single item so if Eigen value is less than 1 then
factors account for less variance the factor is explaining less variances than the single item.
So, one item is one factor and if the Eigen value is less than one that means it is not even
explaining a single item well what we will do is we will continue this same session
in the same thing same factor analysis in the next session now we will take a
break here. Thank you so much.
