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.