What undertone: beauty is in the eye of the

What
is a model? A
Model is an external and explicit representation of a part of reality, as it is
seen by individuals who wish to use this model to understand, change, manage
and control that part of reality.

“Why
are so many models designed and so few used?” is a question often
discussed within the Quantitative Modeling (QM) community. The formulation of
the question seems simple, but the concepts and theories that must be mobilized
to give it an answer are far more sophisticated. Would there be a selection
process from “many models designed” to “few models used”
and, if so, which particular properties do the “happy few” have? This
site first analyzes the various definitions of “models” presented in
the QM literature and proposes a synthesis of the functions a model can handle.
Then, the concept of “implementation” is defined, and we
progressively shift from a traditional “design then implementation”
standpoint to a more general theory of a model design/implementation, seen as a
cross-construction process between the model and the organization in which it
is implemented. Consequently, the organization is considered not as a simple
context, but as an active component in the design of models. This leads
logically to six models of model implementation: the technocratic model, the
political model, the managerial model, the self-learning model, the conquest
model and the experimental model.

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Modeling for Forecasting:
Accuracy and Validation Assessments

Forecasting is a necessary input to planning,
whether in business, or government. Often, forecasts are generated subjectively
and at great cost by group discussion, even when relatively simple quantitative
methods can perform just as well or, at very least; provide an informed input
to such discussions.

Data Gathering for Verification of Model: Data gathering is often considered
“expensive”. Indeed, technology “softens” the mind, in that
we become reliant on devices; however, reliable data are needed to verify a
quantitative model. Mathematical models, no matter how elegant, sometimes
escape the appreciation of the decision-maker. In other words, some people
think algebraically; others see geometrically. When the data are complex or
multidimensional, there is the more reason for working with equations, though
appealing to the intellect has a more down-to-earth undertone: beauty is in the
eye of the other beholder – not you; yourself.

 

 

 

Statistical
Forecasting: The selection and implementation of the
proper forecast methodology has always been an important planning and control
issue for most firms and agencies. Often, the financial well-being of the
entire operation rely on the accuracy of the forecast since such information
will likely be used to make interrelated budgetary and operative decisions in
areas of personnel management, purchasing, marketing and advertising, capital
financing, etc. For example, any significant over-or-under sales forecast error
may cause the firm to be overly burdened with excess inventory carrying costs
or else create lost sales revenue through unanticipated item shortages. When
demand is fairly stable, e.g., unchanging or else growing or declining at a
known constant rate, making an accurate forecast is less difficult. If, on the
other hand, the firm has historically experienced an up-and-down sales pattern,
then the complexity of the forecasting task is compounded.

There are two main
approaches to forecasting. Either the estimate of future value is based on an
analysis of factors which are believed to influence future values, i.e., the
explanatory method, or else the prediction is based on an inferred study of
past general data behavior over time, i.e., the extrapolation method. For example,
the belief that the sale of doll clothing will increase from current levels
because of a recent advertising blitz rather than proximity to Christmas
illustrates the difference between the two philosophies. It is possible that
both approaches will lead to the creation of accurate and useful forecasts, but
it must be remembered that, even for a modest degree of desired accuracy, the
former method is often more difficult to implement and validate than the latter
approach.

Step
4: Selecting a Sample of Respondents

Identify the
accessible population. 
Avoid using samples of convenience. 
Simple random sampling is a desirable method of sampling. 
Systematic sampling is an acceptable method of sampling. 
Stratification may reduce sampling errors. 
Consider using random cluster sampling when every member of a population
belongs to a group. 
Consider using multistage sampling to select respondents from large
populations. 
Consider the importance of getting precise results when determining sample
size. 
Remember that using a large sample does not compensate for a bias in sampling. 
Consider sampling non respondents to get information on the nature of a bias. 
The bias in the mean is the difference of the population means for respondents
and non respondents multiplied by the population nonresponse rate.

General Sampling Techniques

From
the food you eat to the TV you watch, from political elections to school board
actions, much of your life is regulated by the results of sample surveys. In
the information age of today and tomorrow, it is increasingly important that
sample survey design and analysis be understood by many so as to produce good
data for decision making and to recognize questionable data when it arises.
Relevant topics are: Simple Random Sampling, Stratified Random Sampling,
Cluster Sampling, Systematic Sampling, Ratio and Regression Estimation,
Estimating a Population Size, Sampling a Continuum of Time, Area or Volume,
Questionnaire Design, Errors in Surveys.

A
sample is a group of units selected from a larger group (the population). By
studying the sample it is hoped to draw valid conclusions about the larger
group.

A
sample is generally selected for study because the population is too large to
study in its entirety. The sample should be representative of the general
population. This is often best achieved by random sampling. Also, before
collecting the sample, it is important that the researcher carefully and
completely defines the population, including a description of the members to be
included.

Random Sampling: Random sampling of size n from a population size N. Unbiased
estimate for variance of  is
Var()
= S2(1-n/N)/n, where n/N is the sampling fraction. For sampling
fraction less than 10% the finite population correction factor (N-n)/(N-1) is
almost 1.

The
total T is estimated by N. ,
its variance is N2Var().

For
0, 1, (binary) type variables, variation in estimated proportion p is:

S2 = p.(1-p).(1-n/N)/(n-1).

For
ratio r = Sxi/Syi= / ,
the variation for r is

(N-n)(r2S2x + S2y -2
r Cov(x, y)/n(N-1).2.

Stratified Sampling: Stratified sampling can be used whenever the population can
be partitioned into smaller sub-populations, each of, which is homogeneous
according to the particular characteristic of interest.

s = S Wt.
Bxart, over t=1, 2, ..L (strata), and t is SXit/nt.

Its
variance is:

SW2t /(Nt-nt)S2t/nt(Nt-1)

Population
total T is estimated by N. s,
its variance is

SN2t(Nt-nt)S2t/nt(Nt-1).

Since
the survey usually measures several attributes for each population member, it
is impossible to find an allocation that is simultaneously optimal for each of
those variables. Therefore, in such a case we use the popular method of
allocation which use the same sampling fraction in each stratum. This yield
optimal allocation given the variation of the strata are all the same.

Determination
of sample sizes (n) with regard to binary data: Smallest integer greater than
or equal to:

t2 N
p(1-p) / t2 p(1-p) + a2 (N-1)

with
N being the size of the total number of cases, n being the sample size, a the expected error, t being the value
taken from the t distribution corresponding to a certain confidence interval,
and p being the probability of an event.

Cross-Sectional Sampling: Cross-Sectional Study the observation of a defined
population at a single point in time or time interval. Exposure and outcome are
determined simultaneously.

Quota
Sampling: Quota sampling is
availability sampling, but with the constraint that proportionality by strata
be preserved. Thus the interviewer will be told to interview so many white male
smokers, so many black female nonsmokers, and so on, to improve the
representatives of the sample. Maximum variation sampling is a variant of quota
sampling, in which the researcher purposively and non-randomly tries to select
a set of cases, which exhibit maximal differences on variables of interest.
Further variations include extreme or deviant case sampling or typical case
sampling.

What is a statistical instrument? A statistical instrument is any process
that aim at describing a phenomena by using any instrument or device, however
the results may be used as a control tool. Examples of statistical instruments
are questionnaire and surveys sampling.

What is grab sampling technique? The grab sampling technique is to take a
relatively small sample over a very short period of time, the result obtained
are usually instantaneous. However, the Passive Sampling is a
technique where a sampling device is used for an extended time under similar
conditions. Depending on the desirable statistical investigation, the Passive
Sampling may be a useful alternative or even more appropriate than grab
sampling. However, a passive sampling technique needs to be developed and
tested in the field.

Sample Size Determination

The
question of how large a sample to take arises early in the planning of any
survey. This is an important question that should be treated lightly. To take a
large sample than is needed to achieve the desired results is wasteful of
resources whereas very small samples often lead to that are no practical use of
making good decision. The main objective is to obtain both a desirable accuracy
and a desirable confidence level with minimum cost.

Pilot
Sample: A pilot or
preliminary sample must be drawn from the population and the statistics
computed from this sample are used in determination of the sample size.
Observations used in the pilot sample may be counted as part of the final
sample, so that the computed sample size minus the pilot sample size is the
number of observations needed to satisfy the total sample size requirement.

 

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