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Modeling the Growth of Neurology Literature

  • Hadagali, Gururaj S. (Department of Library and Information Science Karnataka University) ;
  • Anandhalli, Gavisiddappa (Department of Library and Information Science Karnataka State Women’s University)
  • Received : 2015.04.08
  • Accepted : 2015.07.21
  • Published : 2015.09.30

Abstract

The word ‘growth’ represents an increase in actual size, implying a change of state. In science and technology, growth may imply an increase in number of institutions, scientists, or publications, etc. The present study demonstrates the growth of neurology literature for the period 1961-2010. A total of 291,702 records were extracted from the Science Direct Database for fifty years. The Relative Growth Rate (RGR) and Doubling Time (Dt.) of neurology literature have been calculated, supplementing with different growth patterns to check whether neurology literature fits exponential, linear, or logistic models. The results of the study indicate that the growth of literature in neurology does not follow the linear, or logistic growth model. However, it follows closely the exponential growth model. The study concludes that there has been a consistent trend towards increased growth of literature in the field of neurology.

1. INTRODUCTION 

One of the features of modern research in recent years has been the spectacular development of scientific discoveries and growth of knowledge, say Gupta et al. (2002). This has caused an unprecedented accumulation of information and has become a major concern for scientists and researchers (Meera & Sangam, 2010). Hence, there is a need to study the growth of scientific knowledge and its dynamics in every field of activity. 

The word ‘growth ’ represents an increase in actual size, implying a change of state. In science and technolgy, growth may imply an increase in number of in stitutions, scientists, or publications, etc. Ravichandra Rao (1998) says that a change in the size of literature over a specific period of time is termed as ‘growth of literature. ’ One of the features of modern research in the twenty-first century has been the unprecedented and spectacular development in scientific inventions, discoveries, and the growth of knowledge. This has caused an unexpected accumulation of information (Gupta et al., 2002). Hence, there is a need to study this growth of knowledge and its dynamics. Price (1966 & 1975) was one of the pioneering researchers who studied the growth of science and found that the exponential model holds well with high accuracy in the majority of growth data of publications. The fitting of growth models, distributions, and curves to the data on exponentially growing literature and identifying the best fitting one to explain the growth of literature is an important aspect of growth study. The present study is aimed to study the growth of neurology literature published in the Science Direct database. 

 

2. REVIEW OF LITERATURE 

The understanding of the process of growth of knowledge in research specialties and its modeling has challenged bibliometricians and sociologists for a long time, say Gupta et al. (1997). Gilberts ’ (1978) work reveals the existing literature on the indicators of growth of knowledge in scientific specialties and lists many ways of measuring it. The analysis of Gupta et al. (1999) suggests that the growth of Indian physics literature follows a logistic model, while the growth of world physics literature is explained by the combination of logistic and power models.

Seetharam and Ravichandra Rao (1999) in their work compare trends in the growth of Food Science and Technology (FST) literature produced by CFTRI scientists, by food scientists in India, and by food scientists of the world, covering a period between 1950 and 1990. Further, the authors identify the best fitting growth models for actual and cumulative growth of data through various growth models. Different approaches are introduced by Gupta and Karisiddappa (2000) in their paper for studying the growth of scientific knowledge as reflected through publications and authors. The selected growth models are applied to the cumulative growth of publications and authors in theoretical population genetics from 1907-1980. It is concluded that the power model is observed to be the only model among the models studied which best explains the cumulative growth of publication and author counts in theoretical population genetics. 

Karki et al. (2000) investigate Indian Organic Chemistry research activity during 1971-1989 using Chemical Abstracts. The authors conclude that the growth trends for India and world for organic chemistry follow the same patterns and the output in the three sub-fields is not going to saturate in the near future. Gupta et al. (2002) apply selected growth models to the growth of publications in six sub-disciplines of social sciences, namely economics, history, political science, psychology, and sociology in the world. The results show that the power model ( α>0, γ>1) followed by logistic models are best describing the cumulative growth of publications in all sub-disciplines. Both power and logistic models are applicable: the power model (as reflected in trend values of α1) and logistic model (as reflected in trend values of α2) in the case of cumulative growth of publications in history, political sciences, and psychology. 
Tsay (2008) explores the characteristics of hydrogen energy literature from 1965-2005 based on the database of Science Citation Index Expanded (SCIE). The study reveals that the cumulative literature on hydrogen energy may be fitted relatively well by an exponential fit. Szydlowski and Krawiec (2009) present a description of knowledge more realistic than simple exponential growth. The study also reveals that the data on symbolic logic exhibit an exponential trend with some periodic oscillation. Ramakrishna (2009) examines the growth of references over the past fifteen years (1994-2008). The results show that the linear growth model provides better fits to the observed data, whereas the exponential model provided the poorest fit. 
Sangam et al. (2010) study the growth and dynamics of Indian and Chinese publications in the field of liquid crystals research (1997-2006) by applying growth models as suggested by Egghe and Ravichandra Rao (1992). The authors conclude that these power and growth models are likely to be fully applicable in the growth of Indian, and linear, power, and growth models applicable in the growth of Chinese liquid crystals literature. Bouabid (2011) proposes a model which is proved to be suitable to represent observed citation distribution over time and to interestingly identify with accuracy when the major loss of citations happens. The model fits the observed data from Science Citation Index (SCI) according to R which is greater than 98.9 %. Zhao and Guan (2012) assess the dynamic associations between scientific activity and technological output. The authors use the simultaneous equations model to analyze the reciprocal dependence between science and technology. The result shows that there is no significant connection between R&D expenditures and actual practices of research in terms of publications. 


3. OBJECTIVES OF THE STUDY 

The specific objectives of the study are 

  1. to study the growth of neurology literature (RGR) and also compare the growth rate as reflected in the Science Direct database among the world, China, and India. 
  2. to examine the Doubling Time (Dt.) of the rology literature. 
  3. to analyze the fit of neurology literature for cumulative numbers of publications in terms of different models. 

 

4. DATA AND METHODOLOGY 

The dataset was collected from the Science Direct database for the period 1961-2010. A total of 291,702 records were received for fifty years. Science Direct is one of the most comprehensive database covering all subjects. Most of the research output on neurology is covered under the Science Direct Database. Hence, the same database is selected as a source for the present study. The keyword ‘neurology ’ has been used for extracting the number of records available in the said database. The retrieved records were examined, classified, and analyzed keeping the objectives in view. Further, the data is analyzed using MS Excel spreadsheet and SPSS software (15 version). Relative Growth Rate (RGR) and Doubling Time (Dt.) of neurology literature have been calculated, supplementing with different growth patterns to check whether the neurology literature is fit for exponential, linear, or logistic models. 

Relative Growth Rate (RGR) and Doubling Time (Dt.)

The Relative Growth Rate (RGR) is the increase in number of articles / pages per unit of time. This definition is derived from the definition of relative growth rates in the study of growth analysis of individual plants and is effectively applied in the field of botany (Hunt, 1978 & 1982; Poorter & Garnier, 1996; Hoffmann & Poorter, 2002). The mean Relative Growth Rate (RGR) over the specific period of interval can be calculated from the following equation: 

\(1-2 \mathrm{R}=\frac{\log _{\mathrm{e} 2} \mathrm{W}-\log _{\mathrm{e} 1} \mathrm{W}}{2^{\mathrm{T}}-1^{\mathrm{T}}}\)


Whereas 

\(1-2R\) = mean relative growth rate over the specific period of interval 

\(\log _{e 1} \mathrm{W}\) = log of initial number of articles 

\(\log _{e 2} \mathrm{W}\) = log of final number of articles after a specific period of interval 

\(2^T-1^T\) = the unit difference between the initial time and the final time 

Doubling Time (Dt.) 

There exists a direct equivalence between the relative growth rate and the doubling time (Bradford, 1934). If the number of articles / pages of a subject double during a given period then the difference between the logarithms of numbers at the beginning and end of this period must be logarithms of number 2. If natural logarithm is used this difference has a value of 0.693. Thus, the corresponding doubling time for each specific period of interval and for both articles and pages can be calculated by the formula; 

\(\text { Doubling Time (Dt.) }=\frac{0.693}{\mathrm{R}}\)


5. RESULTS AND DISCUSSION 

5.1. Year Wise Distribution of Literature (1961-2010) 

Table 1 depicts the year wise distribution of papers in neurology literature. The world output in neurology literature is 286,001 (98.05 %) records and that of China is 3,730 (1.28 %), followed by India with 1,971 (0.68 %) records. A total of 291,702 records were extracted from the database for the period 1961-2010. It is observed that there is a steady growth of publications for world (except 1997) and China. A fluctuating trend was observed for India during the study period. An average of 5,720 papers were published per year at the global level, followed by China ’s average at 74 and India ’s average at 39. The maximum world contribution is observed during 2009 (20,656 publications) and those of China and India were published during 2010 (769 and 219, respectively). China took 24 years to achieve double digit numbers of publications, whereas India took twelve years to achieve the same. However, China took only 20 years to achieve three-digit numbers of publications but India took 33 years to achieve the same. The Relative Growth Rate (RGR) and Doubling Time (Dt.) of China, India, and world is calculated and presented in successive tables. 

 

Table 1. Year-Wise Distribution of Literature (1961-2010) 

Sl. No. Year World India China Total

No. of articles

Percentage

No. of articles

Percentage

No. of articles

Percentage

No. of articles

Percentage
1 1961 400 0.14 5.00 0.26 0 0 405 0.14
2 1962 395 0.14 2.00 0.11 0 0 397 0.14
3 1963 473 0.17 4.00 0.21 0 0 477 0.17
4 1964 624 0.22 2.00 0.11 0 0 626 0.22
5 1965 709 0.25 2.00 0.11 1 0.03 712 0.25
6 1966 673 0.24 1.00 0.06 0 0 674 0.24
7 1967 783 0.28 0.00 0 1 0.03 784 0.27
8 1968 870 0.31 4.00 0.21 0 0 874 0.3
9 1969 926 0.33 6.00 0.31 0 0 932 0.32
10 1970 1,083 0.38 4.00 0.21 1 0.03 1,088 0.38
11 1971 1,169 0.41 5.00 0.26 3 0.09 1,177 0.41
12 1972 1,212 0.43 9.00 0.46 2 0.06 1,223 0.42
13 1973 1,351 0.48 10.00 0.51 1 0.03 1,362 0.47
14 1974 1,428 0.5 9.00 0.46 1 0.03 1,438 0.5
15 1975 1,682 0.59 12.00 0.61 0 0 1,694 0.59
16 1976 1,790 0.63 11.00 0.56 1 0.03 1,802 0.62
17 1977 1,846 0.65 11.00 0.56 0 0 1,857 0.64
18 1978 2,046 0.72 9.00 0.46 1 0.03 2,056 0.71
19 1979 2,168 0.76 10.00 0.51 4 0.11 2,182 0.75
20 1980 2,488 0.87 13.00 0.66 4 0.11 2,505 0.86
21 1981 2,839 1.00 18.00 0.92 3 0.09 2,860 0.99
22 1982 3,264 1.15 13.00 0.66 6 0.17 3,283 1.13
23 1983 3,535 1.24 15.00 0.77 6 0.17 3,556 1.22
24 1984 3,567 1.25 21.00 1.07 8 0.22 3,596 1.24
25 1985 3,962 1.39 18.00 0.92 17 0.46 3,997 1.38
26 1986 4,110 1.44 16.00 0.82 12 0.33 4,138 1.42
27 1987 4,708 1.65 25.00 1.27 13 0.35 4,746 1.63
28 1988 4,496 1.58 25.00 1.27 15 0.41 4,536 1.56
29 1989 4,852 1.7 19.00 0.97 16 0.43 4,887 1.68
30 1990 5,397 1.89 18.00 0.92 21 0.57 5,436 1.87
31 1991 5,696 2.00 25.00 1.27 22 0.59 5,743 1.97
32 1992 6,106 2.14 21.00 1.07 22 0.59 6,149 2.11
33 1993 5,708 2.00 30.00 1.53 27 0.73 5,765 1.98
34 1994 6,904 2.42 36.00 1.83 26 0.7 6,966 2.39
35 1995 6,842 2.4 36.00 1.83 32 0.86 6,910 2.37
36 1996 7,442 2.61 43.00 2.19 29 0.78 7,514 2.58
37 1997 11,698 4.1 44.00 2.24 39 1.05 11,781 4.04
38 1998 7,847 2.75 50.00 2.54 39 1.05 7,936 2.73
39 1999 8,207 2.87 39.00 1.98 68 1.83 8,314 2.86
40 2000 8,964 3.14 62.00 3.15 56 1.51 9,082 3.12
41 2001 8,692 3.04 45.00 2.29 69 1.85 8,806 3.02
42 2002 9,388 3.29 65.00 3.30 82 2.2 9,535 3.27
43 2003 11,374 3.98 71.00 3.61 131 3.52 11,576 3.97
44 2004 12,586 4.41 93.00 4.72 153 4.11 12,832 4.4
45 2005 15,115 5.29 89.00 4.52 203 5.45 15,407 5.29
46 2006 15,153 5.3 149.00 7.56 271 7.27 15,573 5.34
47 2007 16,366 5.73 163.00 8.27 420 11.27 16,949 5.82
48 2008 17,183 6.01 165.00 8.38 529 14.19 17,877 6.13
49 2009 20,656 7.23 209.00 10.61 606 16.25 21,471 7.37
50 2010 19,228 6.73 219.00 11.12 769 20.62 20,216 6.94
  Total 286,001
(98.05)
100 1,971
(0.68)
100.00 3,730
(1.28)
100 291,702
(100)
100


Table 2. Descriptive Statistics of Neurology Literature 

Descriptive Statistics World India China
Mean 5720 39.42 74.6
Standard Error 766.51 7.5276 23.212
Standard Deviation 5420 53.228 164.13
Range 20261 219 769
Minimum 395 0 0
Maximum 20656 219 769

Confidence Level (95.0%)

Kurtosis

Skewness

1,540.4

0.635

1.205

15.127

4.098

2.162

46.646

8.622

2.976

 

5.2. Relative Growth Rate (RGR) and Doubling Time (Dt.) (India) 

The Relative Growth Rate (RGR) and Doubling Time (Dt.) of publications in India have been presented in Table 3. It indicates that the value of Relative Growth Rate (RGR) of publications decreased from 0.337 in the year 1962 to 0.119 in 2010. Simultaneously, the values of Doubling Time (Dt.) increased from 2.056 in 1962 to 5.823 in 2010. It is evident from the study that research in the field of neurology in India has increased over a period of time. 

Table 3. Relative Growth Rate (RGR) and Doubling Time (Dt.) (India) 

Sl. No. Year publications
No. of
Cumulative
publications
no. of
W 1 W 2 RGR Dt. (P)
1 1961 05 05   1.609    
2 1962 02 07 1.609 1.946 0.337 2.056
3 1963 04 11 1.946 2.398 0.452 1.533
4 1964 02 13 2.398 2.565 0.167 4.149
5 1965 02 15 2.565 2.708 0.143 4.846
6 1966 01 16 2.708 2.772 0.064 10.828
7 1967 00 16 2.772 2.772 0.000 00.00
8 1968 04 20 2.772 2.995 0.223 3.107
9 1969 06 26 2.995 3.258 0.263 2.635
10 1970 04 30 3.258 3.401 0.143 4.846
11 1971 05 35 3.401 3.555 0.154 4.500
12 1972 09 44 3.555 3.784 0.229 3.026
13 1973 10 54 3.784 3.988 0.204 3.397
14 1974 09 63 3.988 4.143 0.155 4.471
15 1975 12 75 4.143 4.317 0.174 3.982
16 1976 11 86 4.317 4.454 0.137 5.058
17 1977 11 97 4.454 4.574 0.120 5.775
18 1978 09 106 4.574 4.663 0.089 7.786
19 1979 10 116 4.663 4.753 0.090 7.700
20 1980 13 129 4.753 4.859 0.106 6.537
21 1981 18 147 4.859 4.990 0.131 5.290
22 1982 13 160 4.99 5.075 0.085 8.153
23 1983 15 175 5.075 5.164 0.089 7.786
24 1984 21 196 5.164 5.278 0.114 6.078
25 1985 18 214 5.278 5.366 0.088 7.875
26 1986 16 230 5.366 5.438 0.072 9.625
27 1987 25 255 5.438 5.541 0.103 6.728
28 1988 25 280 5.541 5.634 0.093 7.451
29 1989 19 299 5.634 5.700 0.066 10.500
30 1990 18 317 5.7 5.759 0.059 11.745
31 1991 25 342 5.759 5.835 0.076 9.118
32 1992 21 363 5.835 5.894 0.059 11.745
33 1993 21 384 5.894 5.950 0.056 12.375
34 1994 30 414 5.950 6.026 0.076 9.118
35 1995 36 450 6.026 6.109 0.083 8.349
36 1996 43 493 6.109 6.200 0.091 7.615
37 1997 44 537 6.200 6.200 0.086 8.058
38 1998 50 587 6.286 6.375 0.089 7.786
39 1999 39 626 6.375 6.439 0.064 10.828
40 2000 62 688 6.439 6.534 0.095 7.294
41 2001 45 733 6.534 6.597 0.063 11.000
42 2002 65 798 6.597 6.682 0.085 8.153
43 2003 71 869 6.682 6.767 0.085 8.153
44 2004 93 962 6.767 6.869 0.102 6.794
45 2005 89 1,051 6.869 6.957 0.088 7.875
46 2006 149 1,200 6.957 7.090 0.133 5.210
47 2007 163 1,363 7.090 7.217 0.127 5.456
48 2008 165 1,528 7.217 7.332 0.115 6.026
49 2009 209 1,737 7.332 7.459 0.127 5.456
50 2010 219 1,956 7.459 7.578 0.119 5.823

 

5.3. Relative Growth Rate (RGR) and Doubling Time (Dt.) (China) 

The Relative Growth Rate (RGR) and Doubling Time (Dt.) of publications in China have been presented in Table 4. The study reveals that the value of RGR of publications decreased from 0.693 in 1967 to 0.231 in the year 2010. However, the values of Doubling Time (Dt.) increased from 1.00 in 1967 to 3.00 in 2010. It is also observed from the study that research in the field of neurology in China has increased over a period of time. 

Table 4. Relative Growth Rate (RGR) and Doubling Time (Dt.) (China) 

Sl. No. Year publications
No. of
Cumulative
publications
no. of
W 1 W 2 RGR Dt. (P)
1 1961 00 00   00    
2 1962 00 00 00 00 00 00
3 1963 00 00 00 00 00 00
4 1964 00 00 00 00 00 00
5 1965 01 01 00 00 00 00
6 1966 00 01 00 00 00 00
7 1967 01 02 00 0.693 0.693 1.00
8 1968 00 02 0.693 0.693 00 00
9 1969 00 02 0.693 0.693 00 00
10 1970 01 03 0.693 1.098 0.405 1.711
11 1971 03 06 1.098 1.791 0.693 1.00
12 1972 02 08 1.791 2.079 0.288 2.406
13 1973 01 09 2.079 2.197 0.118 2.406
14 1974 01 10 2.197 2.302 0.105 6.600
15 1975 00 10.000 2.302 2.302 00 00
16 1976 01 11.000 2.302 2.397 0.095 7.294
17 1977 00 11.000 2.397 2.397 00 00
18 1978 01 12.000 2.397 2.485 0.088 7.875
19 1979 04 16.000 2.485 2.772 0.287 2.414
20 1980 04 20.000 2.772 2.995 0.223 3.107
21 1981 03 23.000 2.995 3.135 0.140 4.950
22 1982 06 29.000 3.135 3.367 0.232 2.987
23 1983 06 35.000 3.367 3.555 0.188 3.686
24 1984 08 43.000 3.555 3.761 0.206 3.364
25 1985 17 60.000 3.761 4.094 0.333 2.081
26 1986 12 72.000 4.094 4.276 0.182 2.807
27 1987 13 85.000 4.276 4.442 0.166 4.174
28 1988 15 100.000 4.442 4.605 0.163 4.251
29 1989 16 116.000 4.605 4.753 0.148 4.682
30 1990 21 137.000 4.753 4.919 0.166 4.174
31 1991 22 159.000 4.919 5.068 0.149 4.651
32 1992 22 181.000 5.068 5.198 0.130 5.330
33 1993 27 208.000 5.198 5.337 0.139 4.985
34 1994 26 234.000 5.337 5.455 0.118 5.872
35 1995 32 266.000 5.455 5.583 0.128 5.414
36 1996 29 295.000 5.583 5.687 0.104 6.663
37 1997 39 334.000 5.687 5.811 0.124 5.588
38 1998 39 373.000 5.811 5.921 0.110 6.300
39 1999 68 441.000 5.921 6.089 0.168 4.125
40 2000 56 497.000 6.089 6.208 0.119 5.823
41 2001 69 566.000 6.208 6.338 0.130 5.330
42 2002 82 648.000 6.338 6.474 0.136 5.095
43 2003 131 779.000 6.474 6.658 0.184 3.766
44 2004 153 932.000 6.658 6.837 0.179 3.871
45 2005 203 1135.000 6.837 7.034 0.197 3.517
46 2006 271 1406.000 7.034 7.248 0.214 3.238
47 2007 420 1826.000 7.248 7.509 0.261 2.655
48 2008 529 2355.000 7.509 7.764 0.255 2.717
49 2009 606 2961.000 7.764 7.993 0.229 3.026
50 2010 769 3730.000 7.993 8.224 0.231 3.000

 

6. GROWTH MODELS OF NEUROLOGY LITERATURE 

The authors briefly introduce three growth models, viz. the Linear Growth Model, the Exponential Growth Model, and the Logistic Growth Model, which are generally used in the literature for analyzing the growth of literature in different subjects. 


6.1. Linear Growth Model 


The Linear Growth Model describes growth to be constant or similar from year to year. Thus, a graphic representation of the yearly data accumulated would be a straight line. 

Hypothesis 1 

The growth of publications in the field of neurology literature follows the Linear Growth Model. 

Testing of Hypothesis 

To find out the growth pattern in the field of neurology literature, publications over the last fifty years (1961-2010) were considered as a sample for the analysis in order to fit the data to test whether the growth of literature in neurology follows the Linear Growth pattern or not. The expected numbers of publications (y) or (p) were computed using the following formula:

\(Y=a+b^x\)
Where a and b are constants 
X is the unit of time 


Inference 

The results of a Chi-Square test of goodness of fit 

Fig. 1 Doubling time of Neurology literature

Fig. 1 Doubling time of Neurology literature 

Table 5. Fit into Linear Growth of Neurology Literature 

X Year Observed
publications
no. of
Y (f)
XY X2 Expected
publications
no. of
Y= a+b
P x
f-p (f-p)2 \(\frac{(f-p)^{2}}{p}\)
1 1961                                   405           405 1 -2740.1 3145.1                       9,891,654 -3610
2 1962                                   397           794 4 -2390.2 2787.2                       7,768,484 -3250.1
3 1963                                   477         1,431 9 -2040.3 2517.3                       6,336,799 -3105.8
4 1964                                   626         2,504 16 -1690.4 2316.4                       5,365,709 -3174.2
5 1965                                   712         3,560 25 -1340.5 2052.5                       4,212,756 -3142.7
6 1966                                   674         4,044 36 -990.6 1664.6                       2,770,893 -2797.2
7 1967                                   784         5,488 49 -640.7 1424.7                       2,029,770 -3168.1
8 1968                                   874         6,992 64 -290.8 1164.8                       1,356,759 -4665.6
9 1969                                   932         8,388 81 59.1 872.9                         761,954 12892.6
10 1970                                 1,088       10,880 100 409 679                         461,041 1127.24
11 1971                                 1,177       12,947 121 758.9 418.1                         174,808 230.343
12 1972                                 1,223       14,676 144 1108.8 114.2                           13,042 11.7619
13 1973                                 1,362       17,706 169 1458.7 -96.7                            9,351 6.41043
14 1974                                 1,438       20,132 196 1808.6 -370.6                         137,344 75.9396
15 1975                                 1,694       25,410 225 2158.5 -464.5                         215,760 99.9584
16 1976                                 1,802       28,832 256 2508.4 -706.4                         499,001 198.932
17 1977                                 1,857       31,569 289 2858.3 -1001.3                       1,002,602 350.769
18 1978                                 2,056       37,008 324 3208.2 -1152.2                       1,327,565 413.804
19 1979                                 2,182       41,458 361 3558.1 -1376.1                       1,893,651 532.209
20 1980                                 2,505       50,100 400 3908 -1403                       1,968,409 503.687
21 1981                                 2,860       60,060 441 4257.9 -1397.9                       1,954,124 458.941
22 1982                                 3,283       72,226 484 4607.8 -1324.8                       1,755,095 380.897
23 1983                                 3,556       81,788 529 4957.7 -1401.7                       1,964,763 396.305
24 1984                                 3,596       86,304 576 5307.6 -1711.6                       2,929,575 551.958
25 1985                                 3,997       99,925 625 5657.5 -1660.5                       2,757,260 487.364
26 1986                                 4,138      107,588 676 6007.4 -1869.4                       3,494,656 581.725
27 1987                                 4,746      128,142 729 6357.3 -1611.3                       2,596,288 408.395
28 1988                                 4,536      127,008 784 6707.2 -2171.2                       4,714,109 702.843
29 1989                                 4,887      141,723 841 7057.1 -2170.1                       4,709,334 667.319
30 1990                                 5,436      163,080 900 7407 -1971                       3,884,841 524.482
31 1991                                 5,743      178,033 961 7756.9 -2013.9                       4,055,793 522.863
32 1992                                 6,149      196,768 1024 8106.8 -1957.8                       3,832,981 472.811
33 1993                                 5,765      190,245 1089 8456.7 -2691.7                       7,245,249 856.747
34 1994                                 6,966      236,844 1156 8806.6 -1840.6                       3,387,808 384.69
35 1995                                 6,910      241,850 1225 9156.5 -2246.5                       5,046,762 551.167
36 1996                                 7,514      270,504 1296 9506.4 -1992.4                       3,969,658 417.577
37 1997                               11,781      435,897 1369 9856.3 1924.7                       3,704,470 375.848
38 1998                                 7,936      301,568 1444 10206.2 -2270.2                       5,153,808 504.968
39 1999                                 8,314      324,246 1521 10556.1 -2242.1                       5,027,012 476.219
40 2000                                 9,082      363,280 1600 10906 -1824                       3,326,976 305.059
41 2001                                 8,806      361,046 1681 11255.9 -2449.9                       6,002,010 533.232
42 2002                                 9,535      400,470 1764 11605.8 -2070.8                       4,288,213 369.489
43 2003                               11,576      497,768 1849 11955.7 -379.7                         144,172 12.0589
44 2004                               12,832      564,608 1936 12305.6 526.4                         277,097 22.518
45 2005                               15,407      693,315 2025 12655.5 2751.5                       7,570,752 598.218
46 2006                               15,573      716,358 2116 13005.4 2567.6                       6,592,570 506.91
47 2007                               16,949      796,603 2209 13355.3 3593.7 1.30E+07 967.008
48 2008                               17,877      858,096 2304 13705.2 4171.8 1.70E+07 1269.88
49 2009                               21,471    1,052,079 2401 14055.1 7415.9 5.50E+07 3912.86
50 2010                               20,216    1,010,800 2500 14405 5811 3.40E+07 2344.17

a = -3,090, b = 349.9, X = 10,094.5 
For India: a= -33.25, b= 2.85, X = 408.399 
For China: a=-108.9, b= 7.199, X = 2,982.08 

indicated that the calculated Chi-Square value (X = 10,094.5) is much higher than the critical Chi-Square value of 31.41 for 49 degrees of freedom ( df ) at 0.05 (5%) level of significance. Hence, Hypothesis 1 has been rejected and it is concluded that the growth of literature in neurology does not follow the Linear Growth Model. Similar Growth Models have also been calculated for China and India. In both cases the calculated Chi-Square values (X = 408.399 for India, X = 2,982.08 for China) are much more than the critical Chi-Square value of 31.41 for 49 degrees of freedom ( df ) at 0.05 (5%) level of significance. In both cases the growth of literature in neurology does not follow the Linear Growth Model. The application of the Linear Growth Model in terms of R (0.854) is shown in Fig. 2. The fit statistics indicate a poor fit for the Linear Growth Model in the data sets. A graphical presentation of observed and estimated data values obtained is also shown in Fig. 2. 


6.2. Exponential Growth Model 

The Exponential Growth Model describes an unlimited exponential growth. This model not only provides a rate of growth (the exponential parameter) but also the rate at which the size of the literature doubles, and its doubling time. The exponential growth has been linked to compound interest. 

 

Hypothesis 2 

The growth of publications in the field of neurology literature better fit the Exponential Growth Model. 

 

Testing of Hypothesis 

In order to fit the data to test whether the growth of literature in neurology follows the exponential growth pattern or not, the expected number of publications (y) were computed using the following formula: 

\(Y=K+ab^x\)
Where a and b are constants 
\(K\)= is the asymptote or the upper limit 
\(X\) is the unit of time 

 

E1JSCH_2015_v3n3_45.f002.png 이미지

Fig. 2 Linear growth pattern of neurology literature 

 

Inference 

The results of a Chi-Square test of goodness of fit indicated that the calculated Chi-Square value is (X = 3,631.96), higher than the critical Chi-Square value of 31.41 for 49 degrees of freedom ( \(df\) ) at 0.05 level of significance. Hence, Hypothesis 2 has been rejected and it is concluded that the growth of literature in neurology does not exactly follow the Exponential Growth Model. The Exponential Growth model was also applied for China and India. In both cases the calculated Chi-Square value (X = 100.9477 for India, and X = -5,017.79 for China) is greater than the critical Chi-Square value of 31.41 for 49 degrees of freedom ( df ) at 0.05 (5%) level of significance. In both cases, the growth of literature in neurology does not exactly follow the Exponential Growth Model. However, it nearly follows this growth model. 

However, the application of the Exponential Growth Model in terms of R (0.984) is shown in Fig. 3. 


Table 6. Fit into Exponential Growth of Neurology Literature 

X Year Observed
publications
no. of
Y (f)
Expected no. of
publication
Y=K+abx
f-p (f-p)2 \(\frac{(f-p)^{2}}{p}\)
1 1961 405 273.27 131.73 17,354 63.505
2 1962 397 357.12 39.883 1,590.7 4.4542
3 1963 477 445.31 31.694 1,004.5 2.2557
4 1964 626 538.06 87.941 7,733.7 14.373
5 1965 712 635.61 76.39 5,835.4 9.1807
6 1966 674 738.21 -64.21 4,122.9 5.5849
7 1967 784 846.12 -62.12 3,858.5 4.5603
8 1968 874 959.61 -85.61 7,328.8 7.6373
9 1969 932 1,079 -147 21,601 20.02
10 1970 1,088 1,204.5 -116.5 13,575 11.27
11 1971 1,177 1,336.5 -159.5 25,455 19.045
12 1972 1,223 1,475.4 -252.4 63,712 43.183
13 1973 1,362 1,621.5 -259.5 67,322 41.519
14 1974 1,438 1,775.1 -337.1 113,618 64.008
15 1975 1,694 1,936.6 -242.6 58,869 30.398
16 1976 1,802 2,106.5 -304.5 92,748 44.029
17 1977 1,857 2,285.3 -428.3 183,401 80.254
S1= 17,522        
18 1978 2,056 2,473.2 -417.2 174,062 70.379
19 1979 2,182 2,670.9 -488.9 239,011 89.487
20 1980 2,505 2,878.8 -373.8 139,723 48.535
21 1981 2,860 3,097.5 -237.5 56,387 18.204
22 1982 3,283 3,327.4 -44.44 1,974.8 0.5935
23 1983 3,556 3,569.3 -13.32 177.37 0.0497
24 1984 3,596 3,823.7 -227.7 51,853 13.561
25 1985 3,997 4,091.3 -94.27 8,886.6 2.1721
26 1986 4,138 4,372.7 -234.7 55,070 12.594
27 1987 4,746 4,668.6 77.37 5,986.1 1.2822
28 1988 4,536 4,979.9 -443.9 197,051 39.569
29 1989 4,887 5,307.3 -420.3 176,639 33.282
30 1990 5,436 5,651.6 -215.6 46,485 8.2251
31 1991 5,743 6,013.7 -270.7 73,299 12.189
32 1992 6,149 6,394.6 -245.6 60,324 9.4336
33 1993 5,765 6,795.2 -1,030 1E+06 156.18
34 1994 6,966 7,216.5 -250.5 62,748 8.6951
 S2= 72,401        
35 1995 6,910 7,659.6 -749.6 561,901 73.359
36 1996 7,514 8,125.6 -611.6 374,094 46.039
37 1997 11,781 8,615.8 3,165.2 1E+07 1162.8
38 1998 7,936 9,131.3 -1,195 1E+06 156.46
39 1999 8,314 9,673.5 -1,359 2E+06 191.05
40 2000 9,082 10,244 -1,162 1E+06 131.74
41 2001 8,806 10,843 -2,037 4E+06 382.82
42 2002 9,535 11,474 -1,939 4E+06 327.74
43 2003 11,576 12,138 -561.6 315,402 25.986
44 2004 12,832 12,835 -3.338 11.145 0.0009
45 2005 15,407 13,569 1,837.8 3E+06 248.92
46 2006 15,573 14,341 1,232 2E+06 105.84
47 2007 16,949 15,153 1,796.3 3E+06 212.94
48 2008 17,877 16,006 1,870.6 3E+06 218.6
49 2009 21,471 16,904 4,566.6 2E+07 33.7
50 2010 20,216 17,849 2,367.3 6E+06 313.97
S3= 201,779   3,631.96

 

The fit statistics indicate that it nearly follows the Exponential Growth Model in the data sets. A graphical presentation of observed and estimated data values obtained is also shown in Fig. 3. 

E1JSCH_2015_v3n3_45.f003.png 이미지

Fig. 3 Expontial Growth Pattern of Neurology Literature 

 

6.3. Logistic Growth Model 

Hypothesis 3

The growth of publications in the field of neurology literature follows the Logistic Growth Model. 

 

Testing of Hypothesis 

In order to fit the data to test whether the growth of literature in neurology follows the logistic growth pattern or not, the expected number of publications (y) were computed using the following formula: 

1/Y= K+ab 

Where a and b are constants 
K= is the asymptote or the upper limit 
X is the unit of time 

 

Inference 

The results of the Chi-Square test of goodness of fit show that the calculated Chi-Square value is (\(X^2\) = 5,821.7), much higher than the critical Chi-Square value of 31.41 for 49 degrees of freedom ( \(df\) ) at .05 level of significance. Hence, Hypothesis 3 has been rejected and it is concluded that the growth of literature in neurology does not follow the Logistic Growth Model. 

The Logistic Growth model was also applied for China and India. In both cases the calculated Chi-Square value (\(X^2\) = 199.669504 for India, \(X^2\) = -89,291.47204 for China) is much greater than the critical Chi-Square value of 31.41 for 49 degrees of freedom ( \(df\) ) at 0.05 (5%) level of significance. In both cases the growth of literature in neurology does not follow the Logistic Growth Model. 


7. CONCLUSION 

The bibliometric technique is considered as the most powerful technique for conducting such quantitative studies in this direction. An attempt was made in the present study to measure the trends in various aspects of published literature in the field of neurology literature. 

The study is based on 291,702 research papers published between 1961-2010 as reflected in Science Direct, which is one of the most comprehensive databases covering all subjects. The data were collected, tabulated, and analyzed. The study reveals some factual factorial data through bibliometric analysis. Research articles have been analyzed for finding the year wise trend, Relative Growth Rate, Doubling Time, and examining the different types of growth rate models. The outcome of the present study shows that there is a steady growth of publications for world (except 1997) and China, and a fluctuating trend was observed for India during the study period. Averages of 5,720 papers were published per year at the global level, followed by China ’s average which is 74 and India ’s average at 39. The maximum world contribution is observed during 2009 (20,656 publications) and those of China and India were published during 2010. China took 24 years to achieve double digit numbers of publications, whereas India took twelve years to achieve the same. The research in the field of neurology in India and China has increased over a period of time. The growth of literature in neurology does not follow either the Linear Growth Model or Logistic Growth Model. However, it nearly follows the Expo nential Growth Model. The study concludes that there has been a consistent trend towards increased growth of literature in the field of neurology. 


Table 7. Fit into Logistic Growth of Model of Neurology Literature 

X Year Y 1/Y Expected no. of
publications
1/Y=K+abx
f-p (f-p)2 \(\frac{(f-p)^{2}}{p}\)
1 1961 405 0.00247       469.09 -64.0894 4,107.44948 8.756219
2 1962 397 0.00252       516.22 -119.22 14,213.31824 27.53347
3 1963 477 0.0021       567.97 -90.9688 8,275.322192 14.57003
4 1964 626 0.0016       624.77 1.234815 1.524767453 0.002441
5 1965 712 0.0014       687.07 24.92833 621.4217341 0.90445
6 1966 674 0.00148       755.39 -81.3875 6,623.919766 8.768903
7 1967 784 0.00128       830.25 -46.2497 2,139.03512 2.576376
8 1968 874 0.00114       912.24 -38.2347 1,461.895382 1.602543
9 1969 932 0.00107     1,001.96 -69.9592 4,894.290061 4.88472
10 1970 1,088 0.00092     1,100.08 -12.0806 145.9408986 0.132664
11 1971 1,177 0.00085     1,207.30 -30.2974 917.9336117 0.760321
12 1972 1,223 0.00082     1,324.35 -101.349 10,271.5322 7.755913
13 1973 1,362 0.00073     1,452.01 -90.012 8,102.16351 5.579956
14 1974 1,438 0.0007     1,591.10 -153.102 23,440.37362 14.73216
15 1975 1,694 0.00059     1,742.47 -48.468 2,349.148287 1.348173
16 1976 1,802 0.00055     1,906.99 -104.985 11,021.87541 5.779739
17 1977 1,857 0.00054     2,085.55 -228.553 52,236.28849 25.04674
S1= 0.02076        
18 1978 2,056 0.00049     2,279.08 -223.083 49,766.23102 21.83607
19 1979 2,182 0.00046     2,488.50 -306.495 93,939.25715 37.74942
20 1980 2,505 0.0004     2,714.70 -209.697 43,973.00579 16.19812
21 1981 2,860 0.00035     2,958.58 -98.5786 9,717.739615 3.284597
22 1982 3,283 0.0003     3,220.99 62.01099 3,845.363017 1.193845
23 1983 3,556 0.00028     3,502.72 53.27738 2,838.479262 0.810364
24 1984 3,596 0.00028     3,804.50 -208.496 43,470.7656 11.42615
25 1985 3,997 0.00025     4,126.93 -129.928 16,881.31098 4.090527
26 1986 4,138 0.00024     4,470.51 -332.512 110,564.1821 24.73188
27 1987 4,746 0.00021     4,835.59 -89.5941 8,027.100512 1.660003
28 1988 4,536 0.00022     5,222.35 -686.347 471,072.7936 90.20327
29 1989 4,887 0.0002     5,630.75 -743.747 553,159.502 98.2391
30 1990 5,436 0.00018     6,060.55 -624.547                 390,059 64.3603
31 1991 5,743 0.00017     6,511.26 -768.26                 590,223 90.64654
32 1992 6,149 0.00016     6,982.14 -833.142                 694,125 99.41437
33 1993      5,765 0.00017     7,472.18 -1707.18     2,914,461 390.0416
34 1994      6,966 0.00014     7,980.08 -1014.08     1,028,368 128.8668
S2= 0.00452        
35 1995      6,910 0.00014     8,504.30 -1594.3     2,541,791 298.8831
36 1996      7,514 0.00013     9,043.00 -1529     2,337,849 258.5257
37 1997    11,781 8.50E-05     9,594.13 2186.871     4,782,405 498.472
38 1998      7,936 0.00013    10,155.40 -2219.4     4,925,725 485.0352
39 1999      8,314 0.00012    10,724.30 -2410.34     5,809,753 541.7351
40 2000      9,082 0.00011    11,298.40 -2216.36     4,912,247 434.7753
41 2001      8,806 0.00011    11,874.70 -3068.74     9,417,189 793.0436
42 2002      9,535 0.0001    12,450.80 -2915.75     8,501,603 682.8185
43 2003    11,576 8.60E-05    13,023.60 -1447.64     2,095,662 160.9122
44 2004    12,832 7.80E-05    13,590.70 -758.732       575,674 42.35783
45 2005    15,407 6.50E-05    14,149.50 1257.547     1,581,424 111.7657
46 2006    15,573 6.40E-05    14,697.40 875.6138       766,699 52.1657
47 2007    16,949 5.90E-05    15,232.30 1716.694     2,947,039 193.4729
48 2008    17,877 5.60E-05    15,752.20 2124.788     4,514,724 286.6089
49 2009    21,471 4.70E-05    16,255.40 5215.646    27,202,964 1,673.477
50 2010    20,216 4.90E-05    16,740.20 3475.753    12,080,859 721.6655
S3= 0.00144        

For China: a= 0.5924, b= 0.929, K= 0.03009, X = -89,291.47204 

For India: a= 0.5113, b=0.9077, K = 0.0025, X = 199.669504 


Table 8. Growth Models of Neurology Literature (R value) 

Growth models World China India Remark
Linear 0.826 0.408 0.609 Not fit
Exponential 0.984 0.861 0.765 Not fit
Logistic 0.957 0.721 0.653 Not fit

 

E1JSCH_2015_v3n3_45.f004.png 이미지

Fig. 4 Logistic Growth Model 

 

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