Good morning, welcome to the first lecture
of applied multivariate statistical modeling. Let me tell you the content of this today’s
presentation. So, we will start with introduction, then
variables, data types, data sources, models and modeling followed by principles of modeling,
statistical approaches to model building, multivariate models, some illustrative examples,
three cases followed by references. The entire content will be covered in two hours. Today, I will try to finish up to principles
of modeling, let us start with defining what is applied multivariate statistical modeling?
Let us define whatever you want, first is applied. Now, what do you mean by applied
in science, there is pure science and applied science. Pure science we generally understand
which is basic science, which it basically talks about laws theories and their development,
and their development, definitely it links with the phenomena, which we usually observe
in different aspects of our life. Now, applied science which will use the knowledge of the
pure science and develops something for the benefit of the mankind, so applied science
one of the benefit we can say then when you talk about engineering, it is basically applied.
Now, when I talk about applied statistics what do we mean? I am assuming that you have
knowledge on preliminary basic statistics for example, normal distribution. If you know
normal distribution then also you know the probability density function f x, which is
1 by root over 2 pi sigma square e to the power of minus of x minus mu by sigma square,
where x varies from minus infinity to plus infinity. This is the so called this bell
shaped curve which is developed by Carl Friedrich Gauss.
So, theoretical development so that mean in development of this type of distributions
it is coming under basics. Now, suppose if I want to apply this knowledge to a real life
situation, I can find out a situation like this for example, let us there are three processes,
process A B and C take certain inputs, convert into value added outputs, value added outputs
all cases. Let there are basically three identical machines which is producing steel washers,
steel washers will be shape like this where there is inner diameter ID. There is outer
diameter OD as usual as there will be certain thickness of this washer so I can say T h.
Now, if you produce a large amount of steel washers that means the number of items produced
is large, n is large then the quality characteristic or the characteristics of the steel washer
which is important to the people, the customer ID. If you plot you may get this type of distribution,
which is normally distributed and where you will be getting mean here. There will be definitely
standard deviation for ID. Similarly, for OD similarly, for thickness
now then what you are doing by what is applied here? The production process A for example,
in this case which is producing steel washers each is converted into a statistical process.
In the sense in terms of a distribution like normal distribution, where we are saying that
the production process can be interpreted, the behavior of this process can be interpreted
like this now in order to get it further clarified. If we do like this suppose, this one is for
a production process A and if I say this is for production process B and third one is
this one for production process C, then using these things you will be able to compare.
Compare A B and see their performance in terms of mean and standard deviation. There is possibility
also to see that whether the mean ID produced by C is equal to that of B or A, this type
of comparisons and things possible. So, when we actually when we develop something which
will be useful to the society for the mankind, then we say it is applied. Now, come to the
second word which is basically multivariate. Now, in order to understand multivariate we
have to understand what is variable. I think it is known to you that variable is something
which takes different values that since, I can say takes different values for example,
if I say I D, x is I D inner diameter. Then if I produce one item, I stands for the item
suppose, first item and the I D value it may take value X 1. When we go for second version
it may take X 2. So, if I such way if I go for n washers produced, let X n will come
into consideration. So, these are the values so I D takes different values as a result
I D is a variable here. Now, in statistics we basically talk about two types of variables,
one is fixed variable and the other one is deterministic, sorry random variable.
So, fixed other way we can say deterministic and random we can say probabilistic for example,
if I create another variable which is month it varies probably here but we know all the
months. Suppose, what will be the next month is this month is your December next month
will be January, it is known with certainty that is a deterministic model, but in this
case when you are going to produce a second lot. Suppose, in the second lot even in one
lot what is the value of I D for the second item, or second version it is not known with
certainty, it is governed through probabilistic distribution.
So, that sense that it is random one, we do not know the value exactly and this value
is coming based on certain random experiment. In this case the process which is producing
this item so if I go on saying like this then other variable here is O D. Similarly, other
one is our thickness, now in order to accumulate more than one variable, we will write this
X 1 is I D, X 2 is O D and X 3 is X 1, X 2 and X 3 is thickness the for the first of
first item was produced. Then this will be x 11, second one x 2 1 and n one. Similarly,
for O D x 1 2, x 2 2 like x n 2, and if I go for the X 3 variable that is observed for
first observation, it is x 1 3, second one x 2 3. So, like this x n 3.
So, what we are trying to say here that we are considering three variables X 1, X 2,
X 3 which are nothing but the characteristics of the steel washers in this example which
has inner diameter, which has outer diameter, which has thickness. Now, if you produce n
number of washers then what will happen? Every washers will be having different values for
I D, O D and thickness. So, this is my observation, first one is observation number 1, second
one observation number 2, like that there is observation number n and you see in observation
number 1 if I consider only I D that value is x 1 1, if I consider all three together,
observation 1 takes value x 1 1, x 1 2, x 1 3.
So, similarly if you go on increasing the number of variables up to X p then here it
will be X 1 p, X 2 p like this X n p. Now, each of these as well as this, these are observations
on multiple variables. What do you want to define here? We want to define here multivariate.
So, in order to do so we know variable, deterministic variable, probabilistic, that is random variable
and this is one example where every observation is measured on several variables. Then when
multiple variables come into picture then each observation is a variable vector example,
if I take the ith observation here then x i will be x i 1, x i 2 like this x i p.
So, it is a variable vector that is ith observation on p variables. So, when we deal with this
type of situation where our observations or each of the observations have multiple values
in the sense values on multiple number of variables more than 1 then the situation is
multivariate situation. Now, we define variable, we define multivariate situation, let us understand
what is variate getting me? Instead of saying that x i is like this, if I create something
different based on all those observations that there is linear combination
of variables. For example, here in this in our example there are three variable X 1, X 2 and X 3. If I
create a combination linear combination L C which is beta 1 X 1 plus beta 2 X 2 plus
beta 3 X 3. So, this combiningly will give a quantity or a value or other way we can
also say variable which is we are saying linear combination of variable which is variate,
this is variate and then what is the definition of variate? Linear combination of variables
with empirically written mean weights, that means beta 1, beta 2 and beta 3 will be determined
based on observations. There are n observations so we will be able to determine all those
variables. So, linear combination of or weighted linear
combination of the variables where the weights are determined empirically that is variate.
Now, in this case you can go for one variables, simple one variable that means if I say there
are 3 variables, we are going variable p equal to 1 then that will be uni-variate, when we
go for p equal to greater than equal to 2, that is multivariate. That is what multivariate
usually in statistics books you will be finding univariate statistics. For example, in terms
of normal univariate, normal distribution bivariate, normal distribution multivariate,
normal distribution, so all the bivariate is a part of multivariate, we basically talk
about when univariate means p equal to 1, bivariate means p equal to 2, multivariate
is p greater than equal to 2. So, this is what is multivariate, by word
multivariate we definitely talk something about linear combination of variables where
more than one variable is there, and there are multiple observations, not a single observation,
n number of observations and weights. We determined empirically based on the X observations n
observations that will be collected from the population for which we want to infer something.
All those inference we will discuss later. So, third one, the third issue is statistical.
Now, what is statistical? By statistical we want to say that it is basically using statistics
that is what we want to infer. So, whatever you are developing something
using the statistical tools and taking it, then this development is statistical development.
Now, what is statistics? If I say statistics is nothing but collecting, organizing, analyzing,
then representing and interpreting. What I mean to say collecting data, organizing data,
analyzing data, representing the results and interpreting the results for the population
for which the statistical model, or the statistics is used for some purpose, some purposeful
work will be served. So, when we talk about statistical that means
we talk about the population, then a sample consist of data from the population and we
have some purpose in our mind, objective in our mind. We want to infer something from
of the population and we collect data accordingly we organize the data, we analyze the data,
then we find the result and the result we summarize, and based on this summarization
these findings we infer about the population so that is what is the word statistical is used. Now, last two are but very important one is
the modeling, if you want to understand then first you understand this model. A model there
are many types of model actually very simple one is in our school days. I can remember
we talk about the spring balance like this, so what happened this is a spring, a elastic
one, a load is attached with this is P and it behave in some way, that behavior if you
increase the load, the elongation will be more. If you reduce it will be less.
So, when this is the behavior, this is the spring balance model so to show the behavior
of the spring this type so physical model are developed. So, this is one model which is basically a physical model, which is a physical model. Now, same thing when I came to my engineering studies, I found that there is one important concept called or development or theory called Hooke’s law, where that sigma he stress developed on the spring.
And the elongation strain developed on it they are modeled in such a manner that there
is a relationship like this. This is the range of elasticity, there is another concept called
elasticity. So, what I have seen there or we all have seen there that sigma epsilon.
So, sigma is E epsilon, where E is young modulus or modulus of elasticity. So, this is what
is the theory behind the for elasticity, the area of elastic body when the load is so developed
that each will not go to the yield point or beyond yield point, that is elastic zone.
So, for so long the body is stressed within the within the elastic limit, what will happen
to the property that if you remove the load then it will recover back to the original
position. So, this development is possible because the physics of this particular spring
was known and I can say if we, if I known the modulus of elasticity, I will be able
to tell the relationship between sigma and epsilon. And that time in engineering mechanics
and strength of materials subject we learn on these things, basic mathematical model.
So, in reality you will get different types of mathematical model so that means, what
I mean to say here that a physical model, a mathematical model. Now, what you mean by
statistical model in this case for example, you take a case I think the inner beginning
of this particular study for example, the how did we develop all these things.
So, to experiment I have no idea but suppose you do not know the modulus of elasticity,
but you know that say elastic body and you want to find the relationship in that case
you can do experiment with P, varying P from P 1 to P n. So, that means you will create
n different combinations then you will be getting 0 to n observations and sigma, epsilon
values you will be getting sigma 1, sigma 2, sigma n; three epsilon, epsilon 1, epsilon
2 and then epsilon n. Now, if you plot this what will happen you
may get a plot like this, here it is sigma essentially what is the difference between
this and this here what I am saying, I am straight way without I when you showed you
have shown me this spring balance. Then I immediately say that in elastic body this
is the diagram, because the this Hooke’s law is known to me.
So, mathematics is known to me but in case it is not known I have done several experiments
here. And based on this I am trying, I will do plot like this need not the perfect straight
line, you will get when you go for the empirical relationship. So, this is what is the empirical
1 model? So, this empirical model when we talk about empirical model like this experiment
based or data based models like this, these are basically the statistics, these are all
statistical. So, for me this is for all of us, this is our statistical model.
Now, what is modeling? Then modeling is basically you want to get this type of results, it is
not that a immediately you will get all this there is a process. The steps I have to understand
what is my purpose? I have to understand in one or two full the purpose what are the variables
that are affecting there. I have to identify all the important variables, then I have to
see that how the data on the variable will be collected.
For example, here I shown you the experiment but it may so happen that you cannot do the experiment. So, in that case is there any other way of collecting data for example,
observation someone is interested to see the behavior of a particular animal. So, he cannot
do the experiment may be but there are large number of wild animals of that particular
species. So, we can observe that we are just going
and observing field based so field based observation our this one is our experiment, sometimes
what happened we will go for some naturalistic observations, naturalistic observations which
we talk about the wild animal case field based observation. In the production we go suppose,
the steel washer case go to the production shop, and see that what is happening there
and collect data and accordingly you do some modeling, some naturalistic observations.
So, all those type of data collection mechanism comes under empirical modeling and you have
to understand all these things. So, this is a process, the process of modeling, the process
of model building is called modeling, the process of model building is called of model
building is modeling. So, let us see some of the slides now that
I told that what is multivariate and then what is discussed, why should I use it and
it is a base question and that was should I go for multivariate things? If I can do
by some other way, why multivariate? So, they are some key issues which basically will be
known to you later on that when we talk about multivariate. We talk about multiple variables that is p
cross 1, if p the number of variables then X 1, X 2 like your X p. Now, there is possibility
that these variables are interrelated, there is correlation, one of the easiest way is
correlation in between the variables. So, that means you may be get a correlation matrix
or other way it is basically the covariance between the variables or covariance. By covariance
what I mean to say, if one variable varies there is a possibility that in particular
way that some other variable also varies, then there will be covariance and standardized
covariance is correlation. This is and in the subsequent lectures so covariance that
will be p cross p matrix will come. So, all those things so similarly, the mean
values for all those variables mu 1, mu 2 like mu p, this things will be there. Now,
so my answer to your question is that why should I use it because no physical process
or as such any other systems also, which is characterized by multiple variables. They
should be analyzed other like their behavior should be analyzed by taking into consideration
of all the variables characterizing it. When these variables consider very, very important
for the design development or improvement of the system, for which it is developed.
And as none of as it is obvious there will be covariance or correlation between the variables.
If I go for univariate analysis we will lose substantially the information about the behavior,
because of non-inclusion of the covariance structure. So, we require to control this covariance structure and in multivariate statistics covariance
is a very big issue and which will be found in multivariate distribution. We will be discussing
all this covariance things so it is required. For example, for this case like our this one steel washer, this case the steel washer, three variables are visibly controlling its
quality, inner diameter, outer diameter and thickness. There is chance that inner and
outer diameter will be related, also the thickness in that case the customer will not be able
to apply it or fit it to its own situation if there is huge mismatch.
Now, if we control inner diameter or outer diameter or thickness then what will happen?
Then correlation structure will not be considered and ultimately we will not be able to satisfy
the customer. So, we will be using multivariate statistics or multivariate modeling. When
your system is complex in terms of number of variable it may be in conditions like this,
the correlation structure is intact in order to extract a those correlation information,
you want to extract the pattern from this data that is why you will be using. So, how
do I do it? It is through the third models, so these models will be discussed a little
later. Now, what is next? Next one example, here we are saying that
a particular company operating may be in a city market and we want to see the organizational
health of this company, with respect to profit in rupees million with respect to sales volume
in rupees hundred, absenteeism, machine breakdown and M ratio. Actually, this is schemated intentionally
first one is profit and sales volume, these are the organizational issue that health if
you sell more your profit may be more. And if your profit is more you are healthy in
financially, and another issue is absenteeism, if you are paying substantially and if you
are taking care the well being of the employee’s absenteeism will be less.If you are maintaining the health of the process here we are saying machine, your machine breakdown
will be less. And if you are if you are able to coordinate with customer as well as your
supplier and your M ratio, that much M ratio particularly I say marketing ratio will relate
to the customer and that will be high. So, if this is the case and then we are basically
observing from April, May, June, July that 12 months data and in some units we have measured.
This is nothing but a case of multivariate situation where each of the row like starting
from 1 the first row, these values are talking about multivariate observations for month
April. Similarly, for second these are multivariate
observations so there are we have multivariate observations. Now, you may be may be interested
to know how profit varies over the months, then it will be univariate one if you want
to say that how sales volume vary over the month, it will be also univariate. Now, if
you want to know absenteeism varies over the year over month that is also univariate like this. But if you are interested to see that how
the profit and sales volume covary and they are own variation, then you will have to have to consider two variables. And then should be multivariate situation, sometimes you may
be interested to know how the sales volume will be dependent on absenteeism and machine
breakdown and marketing ratio. Then there must a dependent model and that is the same
multivariate issue. So, this is in that shelf what I am talking about multivariate observations. So, now we have discussed some of the things,
some of the variables and we have seen that we have assigned them some values, but how
where from those values are coming? For example, if I say steel washer the thickness
that mean be the inner or the outer thickness OS, how it is known? So, you have used some
measurement scale to measure this, if I want to say that it may be you have used Vernier
caliper to measure the outer diameter, may be used Vernier caliper to measure the inner
diameter. So, you have used some instrument and as well as you have there is scale of
measurement. In this case the scale is basically length which may be in terms of millimeter.
So, you have to sue some scale of measurement and based on the scale used whatever data
you get those data will be of different types. So, you see this line here, the left side
we are talking about random variables and right hand side we are talking about data
types. I have explained you this random variable earlier, so I will not spend much time here,
but you must please understand one thing that in random variable there will be discrete
and continuous random variable. By discrete random variable we mean to say
that they will take some counted account values like 0, 1, 2 or something like this or January,
February, March something like this, and your continuous case that profit absenteeism breakdown
or what is M ratio here? What is that any value is possible? So, please understand one
thing here, since volume are coming under your discrete because it is countable one but many countable, such count values can also be considered as continuous in any situations.
But any how so there are two types. Now, your data types I told you that what
measurement scale you are using. Based on these data types you will be known, means
that data will be having certain properties because data is nothing but information. How
much information is available with the data getting me, so did it all depends on what
scale you have used to measure this data. So, based on that there are four types of
data, one is nominal data, ordinal data, interval data and ratio data. Let us discuss something about nominal data.
My definition is this provide identity to some items or things is I say the month, the
company, small company that is the I should have shown you that they want to do over the
different months, what is the status. So, the month is a variable starting from January
to December because it changes. So, then it is January and February all those things nothing
but they are the identity of the period of time identity of the particular series.
Suppose, you just think of you are trying to know that some performance or status of
the different department of a for example, IIT so then if I say the department of chemistry,
department of physics, department of mathematics, department of computer science, department
of industrial engineering and management. So, all those things and they are basically
providing identity but we sometimes require this type of data in our to include in our
analysis. So, this is nothing but nominal data. Now, what is the problem with nominal
data? Problem with nominal data is that there is huge computational limitations, because
you cannot do any arithmetic limitations, you cannot add department of chemistry plus
department of physics like this. We cannot say department of chemistry is 1 and department
of physics is 2 and accordingly we will add, we cannot subtract, we cannot multiply, we
cannot make division also this is the problem. Next data type is your ordinal data type.
What is ordinal data type? Suppose, you just see that you have you have travelled in flight
several times may be, or train or some other places or you have gone to the students, and
when you have taken food and you might have seen that you are giving a feedback form.
They are seeing that they are pleased, they have read the in case of hotel food quality,
service quality, room quality all those things in terms of not satisfied.
We are totally unsatisfied to extremely satisfied, this type of scale we have used for example,
for the food case it is taste wise this very good, good or something like this. So, this
type of ordering when order thing is there this is called ordinal data. So, what it does
provide some order or rank to some items or things examples, service quality, it is low
medium or good and computational limitations. Here also we cannot do any arithmetic operations
like your addition, subtraction, multiplication and division. You cannot do then what way
it is better than our nominal data? It is better than nominal data because here you
are getting a order, a rank you are getting. If I say the performance that my student performance
is low, average and very good excellent like this, the person who is getting excellent
is definitely better than the person or the student who got very good. So, I have a ranking
skill here ranking ability with this data. So, ordinal data is rich compared to nominal data. Next data type I said that interval data,
what is interval data? It is basically well understood if we take this example, here temperature
we are measuring using two scales, one is celsius, another only Fahrenheit. In developing
these two scales, Fahrenheit scale as well as your Celsius scale, the reference point
is taken at two different points, means locations. It is not the same you getting me so and if
you see the horizontal lines here you see that 0 degree centigrade, 20 degree centigrade
and 100 degree centigrade. Then the corresponding Fahrenheit will be 32, 70 and 212 Fahrenheit,
understanding? So, there is a range that if I say the difference
from 100 to 0 degree you are getting this range, here are also 212 to 32 the corrseponding
range is this. So, whether we measure in using celsius scale or Fahrenheit scales we will
be getting the equal range. Now, what will happen suppose, I measured temperature today?
Today day temperature is 20 degree centigrade to 30 degree and may be day after tomorrow
21 degree, then if I want to do the averaging I can add them and then divided by 3, that
3 days average I will get if I do the same thing in Fahrenheit. Also it is possible I
can do that similar thing, I can do but what will happen?
Suppose, I want to say that what is the how many times temperature of today is compared
to the tomorrows, yesterday’s temperature. Then if I use Celsius scale and if I divide
22 by 20 and then here it will be it may be 70 and other things, then we will find out
they are not matching. So, that means interval scale is some scale where you will get a interval
data range data and they are all having al, type of continuous properties except and they
can do 3 arithmetic operations very easily, addition, subtraction and multiplication.
But when you do division, you will find out that when you change, it changes the scale.
Ultimately what will happen? You will find that they, so in interval data you cannot
go for division. Interval data division is not possible, all
other arithmetic operations are possible. Let us go to the next slide. Our slide that is we are talking about ratio,
data ratio. Data is something where there is absolute 0 in the scale of measurement. This is 0, if I move towards right suppose
x amount and towards left also x amount then the difference, this difference is same. If
I go for y also, this side also y also that is the same. So, that means if you go in to the left it is that is the same. So, that means if you go in the to the left it is negative,
this side it is positive, but there is absolute 0 in between. So, this 0 is the reference
point not in terms of the Fahrenheit and centigrade scale that where is the two different definition,
it contains absolute 0, highest form of data, sorry. So, ratio data is it contains absolute
0 highest form of data example absenteeism breakdown hours as shown earlier and computational,
all arithmetic operations are possible here. Now, if I go by the order of information available
then definitely your first one is if it is nominal then followed by ordinal, then your
interval, then your ratio. Then definitely in order of increasing information this will
the, this is the case my best data is this, next best is this, next best is this, next
and this is the lowest of information data. So, you know that different data types. Now,
you know that as you will be applying multivariate statistical modeling, you must require full-fledged
data. So, you need to know the data source, primary data collected from the source where
it is generated for example, in the case of a steel washer example, if you collect data
from the production shop and just going there collecting data or that is what is known as
primary data. Suppose, you want to see the behavior of the animals in the jungle go and
observe and then accordingly note down and that will be your primary data.
So, for the production that and that example the profit and sales volume case that is also
primary data. So, long you are collecting from the source, what is secondary data? Secondary
data stored in repository or collected by someone else, you are getting me? So, you
are not collecting, it is already there. We have different sources for example, you may
get the financial data from some sources. And suppose company is maintaining records
of their production and suppose their maintenance or the health of machines and many things.
So, you have not collected so company has stored and you have gone there and collected
these things, or it is better that in a literature you studying something in your own area. You
found that a paper is there where some data is given.
So, this type of data is secondary but secondary data must have must be authentic, in the sense
that reference of the data is available, author references are there, this is that author
literature data but this is definitely as it is done by somebody else. It is not primary,
there you have to rely on the authenticity of the data collected by somebody else. The
tertiary data which is basically a common knowledge type of things.
Suppose, you know you will find many things are there actually when in terms of modeling,
modeling when you start with a subject area you start with this that when your knowledge
is not very clear, you will start with the tertiary sources. And then slowly you go to the secondary source. Finally, when you do actual work you may go for the primary data sources. I told you earlier for this model, let me
repeat this again that model mimics reality that when you develop a model that without
considering the reality, the real thing you are not doing the justice. So, the model reality
so it should be a, it should have real applications that is what is the meaning. For example,
suppose you think of a car which is got with by suppose any they develop, they develop
these things. What I mean to say they develop a model simulation model in computer first
before going for a developing the car, one after the other manufacturing. The car in
the manufacturing shop or there must be some simulation model and means how the car will work. So, that type of things are known as that
means it is a in terms of the reality the car is the real thing. So, your modeling can
be so that is simplest example and that the mathematics is related to the elastic behavior
of it that is the reality. In statistical sense when we talk about the how sales volume
is dependent on other things that is your absenteeism, M ratio and all those things
that also is going to talk about the ways, which show actually in statistical sense,
a model talks about explain the regularity of a phenomena. In Hooke’s law the regularity is so long,
it is within the elastic limit. When the load is released, it will come back to the original
shape that is the regularity. In case of our statistical model building we talk about data
and data is nothing but equal to this is pattern plus error, this pattern is the regularity
pattern or systematic component. So, we must know what is our problem? And accordingly
all data if you collect it and you want to extract pattern from this data. In case of
prediction model suppose you want to predict some y value then with respect to some x values.
And then you will find out there is some linear combination variable that is X beta, then
plus l will be there. This is my regularity or my data.
So, when you repeat similar that similar development under different situations then what will
happen? Then if it performs well under the different situation for which it is developed,
the one day we may say it is a law or a theory like Hooke’s law or Hooke’s or this Hooke’s
law is this, I left there that elasticity thing. So, we all know that Newton’s laws
of motion and we all know that Dalton’s atomic theory and many other things that these
are not one day everything is developed and people accept it. It basically developed at
test stage verified, validated after several years and then other scientist other that
is the researcher, they accepted the fact and then it was applied to different situations
and found that it is working. I told you modeling, also process of building a process, physical,
mathematical and statistical, this is I have already explained to you. I hope that you got the glimpse of actually
the purpose of applied multivariate statistical modeling. Actually, we want to develop empirical
model, those empirical models is these are all data based, data based in the sense that
they contain you have data. And you are going for building models and you are building models,
and to find out the regularity of the data, or the pattern of the data. And show that
you will be able to describe the relationships of the population or the behavior of the population
or system in consideration. You will be able to establish the strength of the relationship,
you will be able to predict something, you may be able to prescribe something also, but
when you talk about a statistical modeling. Usually this is the description and prediction
part is description explanation and prediction this three things come into consideration.
So, slowly you will be knowing different types of statistical all together and you will be
tempted to develop different models, also based on the data whatever available to you
but before model, going for modeling or applying any statistical techniques what is happening?
What is we want to say that you have to have some principles in your mind before going
for this here. I have just jotted down some of the principles which I have taken from
text book by operation research by see what is they said that do not build a complicated
model when a simple one will suffice. For example, suppose if I know the mean value
of the different lots of steel over mid value of a particular characteristics; for example,
the inner diameter of a different your lots produced. And if that suffice my purpose go
for mean, or at max you may require the standard deviation of the inner diameter produced by
the different processes A B C as I told you. So, there you may you do not go for may be
that covariance structure, many other thing. So, you do not go for if it is needed you
go for you are modeling of the problem to fit the technique, many a time I have seen
it my case that there is one model which we will be discussing later on known as structural
equation modeling. The people are using structural model everywhere where a simple regression
model can be. But people are interested to fit the structural equation model.
So, please be little bit of cautious on those things, that model is for problem solving and model
comes from the problem, not to fit a statistical technique. Design phase of modeling must be
conducted rigorously and it will discussed later. What do we mean by design phase? Coming
under study design model should be verified prior to validation. Verification means suppose
you when you collect data you split the data into two halves, one for your training other for test. What other way I can say? One set for model
building, other set for verification and validation basically talks about when you take some new
data again and you find it is working, that is validation. A model should never take in
too literally but many a times what I have found that model there are more many variables,
statistics is taken very in very loose end. So, if there are many variables let us find
the relationship is there or not this type of or whatever variable is there. Let us find
that relationship without considering the purpose. A model should neither be pressed to do nor
criticized for failing to do that for which it was never intended for example, you are
interested to see the relationship between variable of a particular population. Now,
later on you want to see that how I want to predict something, see you developed a model
to see the pattern strength of relationship not to predict. So, why how can your model
will predict which was not intended for, so that is another issue. So, if it fails to
do prediction when it was just to understand the covariance structure, then we should not
criticize for this nor we should not press the model to do it, beware of overselling
a model many a times. We basically make sure of I can say recommendation
based on the model and many of the things basically from common sense, and so that type
of selling I prohibited some of primary benefits of modeling are associated with the process
of developing the model. So, the see as all we of you are busy in learning multivariate
statistics, multivariate modeling. So, do not think that always you will be doing something
great with these type of modeling you are learning. So, the learning process when you
develop something you know the physics of the problem, may be you know the process through
which data is generated, you know how the data to be captured, how the data to be analyzed,
what techniques is applicable. So, this is a entire gamut, so this gamut
of process is very, very important. So, very many fits very, very fits you acquire out
of it a model cannot be any better than information that goes into it. So, you cannot say that
you are using nominal data and you will be basically talking about a model of regression
where y variable is nominal. So, you have to have go for some other type of model for
that may be your regression. So, the information what you are the quality of information what
is fed into that model, that is more important because it if input is not good then output
also, you should not expect good. So, model cannot replace decision maker, getting
me? You cannot think that you are your model is superior than you the decision maker, the
analyst who has having the system knowledge they will act smart. So, they are more important
people, so whatever you develop, whatever you do for, what purpose you are developing,
all these things. So, that is in your brain, in it is the root what work there so better
than any model. So, in this case what I want to say that you please take all those issues
what I have discussed, the principles particularly in this series and accordingly develop the
model and today it is up to these. Next class, we will be studying the statistical approach to problem. Thank you for your patience.
