PREPARE CONCEPTUAL FRAMEWORK OF MAXIMUM LIKELIHOOD ESTIMATOR, LINEAR DEPENDENT MODEL AND PROBIT MODEL. COLLECT THE DATA OF 100 CROSS-SECTIONAL DATA AND ANALYSE DATA BY USING PROBIT MODEL:
Samita
Paudel
MSc. Agricultural Economics
Institute
of Agriculture and Animal Science
Kirtipur, Kathmandu
INTRODUCTION:
Probit
regression, also called a probit model, is used to model dichotomous or binary
outcome variables. Probit analysis developed from the need to
analyze qualitative (dichotomous or polytomous) dependent variables within the
regression framework. Many response variables are binary by nature (yes/no),
while others are measured ordinally rather than continuously (degree of
severity). Ordinary least squares (OLS) regression has been shown to be
inadequate when the dependent variable is discrete. Probit or logit analyses
are more appropriate in this case. The PROBIT procedure computes maximum
likelihood estimates of the parameters Ɓ and C of the probit equation using a
modified Newton-Raphson algorithm. When the response Y is binary, with values 0
and 1, the probit equation is:
B- is
a vector of parameter estimate
F
-is a cumulative distribution function (the normal, logistic, or extreme value
X -is a vector of
explanatory variables
P- is the probability of
a response
C- is the natural
(threshold) response rate
Notice that PROC PROBIT,
by default, models the probability of the lower response levels. The choice of
the distribution function F (normal for the probit model, logistic for the
logit model, and extreme value or Gompertz for the gompit model) determines the
type of analysis. For most problems, there is relatively little difference
between the normal and logistic specifications of the model. Both distributions
are symmetric about the value zero. The extreme value (or Gompertz)
distribution, however, is not symmetric, approaching 0 on the left more slowly
than it approaches 1 on the right. You can use the extreme value distribution
where such asymmetry is appropriate.
For ordinal response
models, the response, Y, of an individual or an experimental unit may be
restricted to one of a (usually small) number, k + 1(k >_ 1), of ordinal
values, denoted for convenience by 1;: : :; k; k + 1.
A probit model
is a popular specification for an ordinal or a binary response
model. As such it treats the same set of problems as logistic
regression using similar techniques. The probit model, which employs
a probit link function, is most often estimated using the
standard maximum likelihood procedure, such an estimation being
called a probit regression.
Probit model, in which
the error term has the normal distribution. Given the assumption of normality,
the probability that Ii * is less
than or equal to Ii can be computed
from the standard normal cumulative distribution function (CDF) 13 as:
Where Pr (Y|X) means the
probability that an event occurs (i.e. smoking) given the values of the X
variables and where Z is the standard normal variable (i.e. a normal variable
with zero mean and unit variance). F is the standard normal CDF, which in the
present context can be written as:
Since P represents the
probability that a person smokes, it is measured by the area of the standard
CDF curve from -ꚙ to Ii. In the present context, F (Ii) is called the probit
function. Although the estimation of the utility index BX and the Bs is rather
complicated in the probit model, the method of maximum likelihood can be used
to estimate them.
OBJECTIVES:
Ø To prepare conceptual framework of maximum likelihood
estimator of probit model
Ø To collect cross sectional data and analyze data
through probit regression
LITERATURE REVIEW:
The adoption of new
technology is an effective way to increase agriculture production and
productivity although it is relatively complicate process. In the agricultural
sector, widening of adoption of new technology by all farmers is rare due to
the various deterrents to adoption imposed by various economic, social,
physical, and technical factors .There are several socioeconomic factors influencing the rate of
adoption, continuation or discontinuation of new technologies in agriculture
sector. Ghimire and Huang (2015) found the positive influence between
household wealth index and adoption and intensity of adoption of improved maize
varieties. The factors most strongly related to adoption were farmers’ ages,
with older farmers being less likely to adopt, possibly because of risk
aversion. Education and extension services positively influenced adoption among
poorly endowed households, implying that increased awareness and information
reduced risk aversion and motivated farmers to adopt new technology. Similarly,
Ransom et al. (2003) found significant and positive relation between adoptions
of improved maize varieties with khet land area, ethnic group, years of
fertilizer use, off-farm income, and contact with extension. Extension services
seem to have the biggest impact on technology adoption as farmers who have contacts with extension workers are more
likely to hear about improved varieties and thus adopt new agricultural
technologies. Mishra et al. (2017) reported household head, age of the
household head, full time farm worker Training Received or not, Farm Size, head
Contact with extension agents, participation in collective action, Source seed
availability, Contact with processor were
positively influencing adoption whereas, Distance to market/road and off farm
income were influencing negatively on adoption of improved maize varieties.
Similarly, Paudel and Matsuoka (2008)
found significant influences between winter maize cultivation, education of the
household head, lowland area, upland area as well as access to credit and
extension services with adoption of IMVs. Subedi et al. (2017) conducted a
survey on Socio-economic assessment on maize production and adoption of open
pollinated improved varieties in Dang, Nepal and reported that the adoption of
improved maize variety is determined by several factors like ethnicity, gender
of the household head, area under improved maize, number of visits by farmer to
agro vets and seed source. Among the variables ethnicity, area under IMVs and
extension service were found highly positively influencing compared to others.
METHODOLOGY
RESULT AND DISCUSSION:
CONCEPTUAL FRAMEWORK:
Conceptual framework are formulated
to explain, predict, and understand phenomena and, in many cases, to challenge
and extend existing knowledge within the limits of critical bounding
assumptions. The conceptual framework is the structure that can hold or support
a theory of a research study. It introduces and describes the concept of the
theory that explains why the research problem under study exists. Conceptual
framework for the probit model can be better understand through the example as:
Suppose
a response variable Y is binary, that is it can have only two possible
outcomes which we will denote as 1 and 0. For example, Y may
represent presence/absence of a certain condition, success/failure of some
device, answer yes/no on a survey, etc. We also have a vector
of regressors X, which are assumed to influence the
outcome Y. Specifically, we assume that the model takes the form
Where Pr denotes probability, and Φ is the Cumulative
Distribution Function (CDF) of the standard normal distribution. The
parameters β are typically estimated by maximum
likelihood.
It is possible to motivate the probit model as a latent
variable model. Suppose there exists an auxiliary random variable
Where ε ~ N
(0, 1). Then Y can be viewed as an indicator for whether this
latent variable is positive:
The use of the standard normal distribution causes
no loss of generality compared with the use of a normal distribution
with an arbitrary mean and standard deviation, because adding a fixed amount to
the mean can be compensated by subtracting the same amount from the intercept,
and multiplying the standard deviation by a fixed amount can be compensated by
multiplying the weights by the same amount.
To see that the two models are equivalent, note that
MAXIMUM LIKELIHOOD
ESTIMATION:
The estimator β^which maximizes this function
will be consistent, asymptotically normal and efficient provided
that E [XX'] exists and is not singular. It can be shown that this
log-likelihood function is globally concave in β, and
therefore standard numerical algorithms for optimization will converge rapidly
to the unique maximum.
Asymptotic distribution for β^ is given by:
Where,
DESCRIPTIVE SUMMARY AND INTERPRETATION:
MODEL SPECIFICATION:
• Pi=Pi(Y
= 1) = f (β + β1X1 + β2X2 + β3X3
+ β4X4+ β5X5 )
• where,
Pi(Y = 1) is probability of adoption of Improved varieties
• X1,
Gender of household head (male=1, female=0)
• X2, Land holding (Ropani)
• X3,
Knowledge of improved varieties (1=yes,0= no)
• X4,Off
farm income (1=yes,0= no)
• X5,
Agri-income (Rs)
Number of observation =
100
LR chi2 (5) =
36.75
Prob > chi2 =
0.0000
Pseudo R2 =
0.2730
Log likelihood = -48.927356
|
Coefficient
|
Chi-sq. values (Wald test)
|
P-value
|
|
|
Probit model (Overall)
|
|
23.88964029
|
|
|
Gender
|
-0.2319692
|
0.757002491
|
0.425
|
|
Off farm income
|
0.2858065
|
0.70711668
|
0.399
|
|
Land holding
|
-0.0367892
|
0.057349991
|
0.856
|
|
Knowledge
|
0.8961266
|
7.695912748
|
0.003*
|
|
Agri-income
|
0.000154
|
5.22446201
|
0.008*
|
In running probit
regression between dependent variable (adoption of improved varieties) with
five different explanatory variable. The model chi square value was 36.75 which
is significant at 1 % level of significance indicating the model fit is good.
The coefficient of Agriculture income is 0.000154
and its p value (0.008) is less than 0.05 at the 5% level of significance. This
means that an increase in agriculture income increases the predicted
probability of adoption of improved varieties by farmers. Wealthier the
households more willing to adopt improved maize varieties as they have better
ability to cope with production and price risks (Ghimire and Huang, 2015). The gender, off farm income, landholding
size has no significant influence in adoption of improved varieties at 5% level
of significance, since their p value are more than 0.05. The coefficient
knowledge of improved varieties is 0.8961266 and its p value (0.003) is less
than 0.05 at the 5% level of significance. This means that an increase in
knowledge of improved varieties in farmers increases the probability of
adoption of improved varieties by farmers. Education was found positive and
significant in a large number of adoption studies. (Ghimire and Huang, 2015) reported that the one additional increase
in year of education of household head was found increasing the probability of
adopting IMVs by 2 %, the reason behind this is that educated farmers have
better information and risk bearing capacity than less educated ones. This
result is supported by previous literature (Paudel and Matsuoka, 2008)
suggesting that adoption depends on the decision makers’ educational
level and access to information because education is thought to create a
favorable mental attitude for the acceptance of new practices. However (Mishra
et al., 2017) found no significant influence of education of house hold head in
adoption of improved maize variety.
Improving the production of cereal crops
is one of the most important strategy for maintaining food security and
decreasing import situation in Nepal. It would be a wise decision by farmers to
adopt improved variety of crops, as improved variety responds better to the
inputs used and yields higher compared to local. However, farmer’s decision on
adoption of improved varieties is influenced by several factors. From our
study, agricultural income and knowledge of improved varieties are
significantly influencing the adoption process of improved varieties. If local
farmers have knowledge on improved varieties, then they will quickly adopt this
type of technologies and with the increase in agriculture income the farmer’s
adoption of improved varieties increases. Researchers are suggested to study
the influences of communication channels and farmers’ perception on adoption of
improved varieties which are equally important to the socio-economic variables.
REFERENCES:
Besley, T. and
A.Case.1993. Modeling technology adoption in developing countries. The American
Economic Review. 83(2).pp.396–402.doi:
10.2307/2117697.
Ghimire, R. and W.C.Huang. 2015. Household wealth and
adoption of improved maize varieties in Nepal: a double-hurdle approach. Food
Security, 7(6). pp.1321-1335. doi: 10.1007/s12571-015-0518-x
Kassie, M., M.
Jaleta., B. Shiferaw., F. Mmbando and H. Groote De.2012.Improved Maize
Technologies and Welfare Outcomes In: Smallholder Systems: Evidence From
Application of Parametric and Non-Parametric Approaches. Selected Paper IAAE
Triennial Conference, Foz do Iguaçu, Brazil, 18–24 August 2012.
KC,
G., T.B.Karki., J.Shrestha, and B.B.Achhami.2015. Status and prospects of maize
research in Nepal. Journal of Maize Research and Development.1 (1).pp.1-9.
Khatri-Chhetri,
D.2015. Maize seed value chains in the Hills of Nepal- Linking small farmers to
markets. Paper presented at Regional Workshop on Agricultural Transformation:
Challenges and Opportunities in South Asia, Kathmandu, Nepal, February 13,
2015.
Mishra,
R. P., G.R. Joshi and Dilli KC.2017. Adoption of improved variety maize seed
production among rural farm households of western Nepal. International Journal
of Agriculture Innovations and Research. 6(2), 2319-1473.pp.423-431
Paudel,
P. and A. Matsuoka.2008.Factors influencing of improved maize varieties in
Nepal: A case study of Chitwan district. Australian Journal of Basic and
Applied Sciences. 2(4).pp.823-834.
Ransom,
JK., K. Paudyal and K.
Adhikari.2003.Adoption of improved maize varieties in the hills of Nepal.
Journal of the International Association of Agricultural Economics,
29(3).pp.299-305.
Rogers,
E.M. and Shoemaker.1971.Communication of innovations: A cross culture approach.
The Free Press, Collier Macmillan publishing Inc. NY. Pp.11-28.
Sharma,
V. P.and A. Kumar.2000. Factors influencing adoption of agroforestry programme:
a case study from North-West India. Indian Journal of Agricultural Economics,
55(3).pp.500–510.
Subedi,
Sanjiv. Yuga Nath Ghimire and Deepa Devkota.2017. Socio-economic assessment on
maize production and adoption of open pollinated improved varieties in Dang,
Nepal. Journal of Maize Research and Development. 3 (1).pp.17-27
DOI:http://dx.doi.org/10.3126/jmrd.v3i1.18916
ANNEX:
Table: The survey data on factors influencing adoption
of improved varieties in Lamjung district
|
ID
|
Agriculture income
|
Gender
|
Off-farm
income
|
Adoption of
improved varieties
|
Size of Land hold
(ropani)
|
Knowledge about improved variety
|
|
1
|
35000
|
0
|
1
|
0
|
1
|
0
|
|
2
|
60000
|
1
|
0
|
0
|
2
|
0
|
|
3
|
100000
|
1
|
1
|
0
|
3
|
0
|
|
4
|
100000
|
1
|
1
|
1
|
3
|
1
|
|
5
|
40000
|
0
|
0
|
0
|
2
|
0
|
|
6
|
65000
|
1
|
0
|
0
|
2
|
1
|
|
7
|
120000
|
1
|
1
|
1
|
4
|
1
|
|
8
|
100000
|
0
|
1
|
1
|
4
|
1
|
|
9
|
120000
|
0
|
0
|
1
|
4
|
0
|
|
10
|
130000
|
0
|
1
|
1
|
4
|
1
|
|
11
|
30000
|
1
|
1
|
0
|
4
|
0
|
|
12
|
45000
|
0
|
0
|
0
|
1
|
0
|
|
13
|
30000
|
1
|
0
|
1
|
1
|
0
|
|
14
|
40000
|
0
|
1
|
0
|
2
|
1
|
|
15
|
40000
|
0
|
0
|
1
|
2
|
1
|
|
16
|
50000
|
1
|
1
|
0
|
1
|
1
|
|
17
|
80000
|
1
|
0
|
1
|
2
|
0
|
|
18
|
60000
|
0
|
0
|
0
|
2
|
1
|
|
19
|
90000
|
1
|
1
|
1
|
3
|
1
|
|
20
|
60000
|
1
|
1
|
0
|
3
|
1
|
|
21
|
80000
|
0
|
1
|
1
|
3
|
1
|
|
22
|
55000
|
0
|
0
|
0
|
2
|
1
|
|
23
|
100000
|
1
|
1
|
1
|
4
|
1
|
|
24
|
100000
|
0
|
1
|
0
|
3
|
1
|
|
25
|
50000
|
1
|
1
|
0
|
2
|
1
|
|
26
|
90000
|
0
|
1
|
1
|
4
|
1
|
|
27
|
120000
|
0
|
1
|
0
|
5
|
1
|
|
28
|
60000
|
1
|
0
|
0
|
3
|
0
|
|
29
|
70000
|
0
|
0
|
0
|
2
|
1
|
|
30
|
60000
|
1
|
0
|
1
|
2
|
1
|
|
31
|
42000
|
0
|
0
|
0
|
1
|
1
|
|
32
|
28000
|
0
|
1
|
0
|
1
|
0
|
|
33
|
32000
|
1
|
1
|
1
|
4
|
1
|
|
34
|
45000
|
1
|
1
|
0
|
3
|
1
|
|
35
|
20000
|
0
|
0
|
0
|
1
|
0
|
|
36
|
60000
|
1
|
1
|
0
|
2
|
0
|
|
37
|
80000
|
1
|
1
|
1
|
2
|
1
|
|
38
|
60000
|
0
|
1
|
0
|
2
|
0
|
|
39
|
70000
|
1
|
1
|
0
|
3
|
1
|
|
40
|
20000
|
0
|
0
|
0
|
1
|
0
|
|
41
|
100000
|
0
|
1
|
1
|
1
|
1
|
|
42
|
150000
|
1
|
1
|
1
|
5
|
1
|
|
43
|
60000
|
0
|
1
|
0
|
2
|
0
|
|
44
|
120000
|
0
|
1
|
1
|
4
|
1
|
|
45
|
30000
|
1
|
0
|
0
|
1
|
0
|
|
46
|
45000
|
0
|
0
|
0
|
1
|
1
|
|
47
|
80000
|
1
|
1
|
1
|
2
|
1
|
|
48
|
150000
|
1
|
1
|
1
|
3
|
1
|
|
49
|
140000
|
1
|
1
|
0
|
3
|
1
|
|
50
|
65000
|
0
|
0
|
0
|
2
|
0
|
|
51
|
35000
|
1
|
0
|
0
|
1
|
0
|
|
52
|
45000
|
0
|
1
|
1
|
1
|
1
|
|
53
|
24000
|
0
|
0
|
0
|
1
|
0
|
|
54
|
25000
|
1
|
0
|
0
|
1
|
0
|
|
55
|
80000
|
1
|
1
|
1
|
2
|
1
|
|
56
|
60000
|
0
|
0
|
0
|
2
|
0
|
|
57
|
100000
|
1
|
0
|
1
|
3
|
1
|
|
58
|
120000
|
0
|
1
|
1
|
3
|
1
|
|
59
|
60000
|
1
|
0
|
0
|
2
|
0
|
|
60
|
120000
|
1
|
0
|
1
|
2
|
1
|
|
61
|
180000
|
0
|
1
|
1
|
4
|
0
|
|
62
|
50000
|
0
|
1
|
0
|
3
|
0
|
|
63
|
80000
|
1
|
0
|
0
|
2
|
1
|
|
64
|
35000
|
1
|
0
|
0
|
1
|
0
|
|
65
|
50000
|
1
|
0
|
0
|
2
|
0
|
|
66
|
80000
|
0
|
1
|
1
|
2
|
1
|
|
67
|
80000
|
1
|
1
|
1
|
3
|
0
|
|
68
|
42000
|
0
|
0
|
0
|
3
|
0
|
|
69
|
50000
|
0
|
1
|
0
|
3
|
0
|
|
70
|
45000
|
0
|
0
|
0
|
1
|
1
|
|
71
|
38000
|
0
|
0
|
1
|
1
|
0
|
|
72
|
100000
|
1
|
1
|
0
|
3
|
0
|
|
73
|
40000
|
0
|
0
|
0
|
3
|
1
|
|
74
|
50000
|
0
|
0
|
1
|
2
|
1
|
|
75
|
48000
|
1
|
0
|
0
|
1
|
0
|
|
76
|
25000
|
0
|
1
|
1
|
1
|
0
|
|
77
|
45000
|
1
|
0
|
0
|
1
|
1
|
|
78
|
40000
|
1
|
0
|
1
|
1
|
1
|
|
79
|
42000
|
1
|
1
|
0
|
3
|
1
|
|
80
|
32000
|
1
|
0
|
0
|
1
|
0
|
|
81
|
36000
|
0
|
0
|
0
|
1
|
1
|
|
82
|
45000
|
0
|
1
|
1
|
3
|
1
|
|
83
|
60000
|
0
|
1
|
0
|
2
|
0
|
|
84
|
50000
|
1
|
1
|
0
|
2
|
0
|
|
85
|
40000
|
1
|
0
|
0
|
2
|
0
|
|
86
|
80000
|
0
|
1
|
1
|
3
|
1
|
|
87
|
25000
|
0
|
0
|
0
|
1
|
0
|
|
88
|
120000
|
0
|
1
|
1
|
3
|
1
|
|
89
|
160000
|
1
|
1
|
0
|
4
|
0
|
|
90
|
160000
|
0
|
1
|
1
|
4
|
1
|
|
91
|
65000
|
1
|
0
|
0
|
2
|
0
|
|
92
|
150000
|
0
|
1
|
1
|
4
|
1
|
|
93
|
60000
|
1
|
0
|
0
|
2
|
0
|
|
94
|
120000
|
0
|
1
|
1
|
4
|
0
|
|
95
|
120000
|
0
|
1
|
1
|
4
|
1
|
|
96
|
25000
|
1
|
0
|
0
|
1
|
0
|
|
97
|
38000
|
1
|
0
|
0
|
1
|
0
|
|
98
|
45000
|
1
|
1
|
1
|
2
|
1
|
|
99
|
55000
|
1
|
1
|
0
|
1
|
0
|
|
100
|
50000
|
1
|
1
|
0
|
2
|
1
|
Table: STATA showing the probit regression of survey
data on Adoption of improved varieties by farmers of Lamjung district
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