Academic literature on the topic 'Ordinal data analysis'

This thesis presents methodology to analyse repeated ordered categorical data (repeated ordinal data), under the assumption that measurements arise as discrete realisations of an underlying (latent) continuous distribution. Two sets of estimation equations, called quasiestimation equations or QEEs, are presented to estimate the mean structure and the cutoff points which define boundaries between different categories. A series of simulation studies are employed to examine the quality of the estimation processes and of the estimation of the underlying latent correlation structure. Graphical studies and theoretical considerations are also utilised to explore the asymptotic properties of the correlation, mean and cutoff parameter estimates. One important aspect of repeated analysis is the structure of the correlation and simulation studies are used to look at the effect of correlation misspecification, both on the consistency of estimates and their asymptotical stability. To compare the QEEs with current methodology, simulations studies are used to analyse the simple case where the data are binary, so that generalised estimation equations (GEEs) can also be applied to model the latent trend. Again the effect of correlation misspecification will be considered. QEEs are applied to a data set consisting of the pain runners feel in their legs after a long race. Both ordinal and continuous responses are measured and comparisons between QEEs and continuous counterparts are made. Finally, this methodology is extended to the case when there are multivariate repeated ordinal measurements, giving rise to inter-time and intra-time correlations.

Many promising Phase II trials have been carried out in head injury however to date there has been no successful translation of the positive results from these explanatory trials into improved patient outcomes in Phase III trials. Many reasons have been hypothesised for this failure. Outcomes in head injury trials are usually measured using the five point Glasgow Outcome Scale. Traditionally the ordinality of this scale is disregarded and it is dichotomised into two groups, favourable and unfavourable outcome. This thesis explores whether suboptimal statistical analysis techniques, including the dichotomisation of outcomes could have contributed to the reasons why Phase III trials have been unsuccessful. Based on eleven completed head injury studies, simulation modelling is used to compare outcome as assessed by the conventional dichotomy with both modelling that takes into account the ordered nature of the outcome (proportional odds modelling) and modelling which individualises a patient’s risk of a good or poor outcome ( the ‘sliding dichotomy’). The results of this modelling show that both analyses which use the full outcome scale and those which individualise risk show great efficiency gains (as measured by reduction in required sample sizes) over the conventional analysis of the binary outcome. These results are consistent both when the simulated treatment effects followed a proportional odds model and when they did not. Consistent results were also observed when targeting or restricting improvement to groups of subjects based on clinical characteristics or prognosis. Although proportional odds modelling shows consistently greater sample size reductions the choice of whether to use proportional odds modelling or the sliding dichotomy depends on the question of interest.

Abstract The use of complex networks for time series analysis has recently shown to be useful as a tool for detecting dynamic state changes for a wide variety of applications. In this work, we implement the commonly used ordinal partition network to transform a time series into a network for detecting these state changes for the simple magnetic pendulum. The time series that we used are obtained experimentally from a base-excited magnetic pendulum apparatus, and numerically from the corresponding governing equations. The magnetic pendulum provides a relatively simple, non-linear example demonstrating transitions from periodic to chaotic motion with the variation of system parameters. For our method, we implement persistent homology, a shape measuring tool from Topological Data Analysis (TDA), to summarize the shape of the resulting ordinal partition networks as a tool for detecting state changes. We show that this network analysis tool provides a clear distinction between periodic and chaotic time series. Another contribution of this work is the successful application of the networks-TDA pipeline, for the first time, to signals from non-autonomous nonlinear systems. This opens the door for our approach to be used as an automatic design tool for studying the effect of design parameters on the resulting system response. Other uses of this approach include fault detection from sensor signals in a wide variety of engineering operations.

The article is devoted to the analysis of the digital content of publications of one issue of the daily All-Ukrainian newspaper “Den” (March 13-14, 2020). The author aims to identify the main thematic groups of digital designations, as well as to consider cases of justified and unsuccessful use of digital designations. Applying the content analysis method, the author identifies publications that contain numerical notations, determines the number of such notations and their affiliation with the main subject groups. Finds that the thematic group of digital designations “time” (58.6% of all digital designations) is much more dominant. This indicates that timing is the most important task of a newspaper text. The second largest group of digital designations is “measure” (15.8% of all digital designations). It covers dimensions and proportions, measurements of distance, weight, volume, and more. The third largest group of digital signage is money (8.2% of all digital signage), the fourth is numbering (5.2% of all digital signage), and the fifth is people (4.4% of all digital signage). The author focuses on the fact that the digits of the journalist’s text are both a source of information and a catch for the reader. Vivid indicators give the text a sense of accuracy. When referring digital data to the text, journalists must adhere to certain rules for the writing of ordinal numbers with incremental graduation; submission of dates; pointing to unique integers that are combined (or not combined) with units of physical quantities, monetary units, etc.; writing a numerator at the beginning of a sentence; unified presentation of data. This will greatly facilitate the reader’s perception of the information.

Climate change will increase weather induced risks to forests, and thus effective adaptation measures are needed. In Säätyö project funded by the Ministry of Agriculture and Forestry, we have summarized the data that facilitate adaptation measures, developed weather and climate services that benefit forestry, and mapped what kind of new weather and climate services are needed in forestry. In addition, we have recorded key further development needs to promote adaptation. The Säätyö project developed a service product describing the harvesting conditions of trees based on the soil moisture assessment. The output includes an analysis of the current situation and a 10-day forecast. In the project we also tested the usefulness of long forecasts beyond three months. The weather forecasting service is sidelined and supplemented by another co-operation project between the Finnish Meteorological Institute and Metsäteho called HarvesterSeasons (https://harvesterseasons.com/). The HarvesterSeasons service utilizes long-term forecasts of up to 6 months to assess terrain bearing conditions. A test version of a wind damage risk tool was developed in cooperation with the Department of Forest Sciences of the University of Eastern Finland and the Finnish Meteorological Institute. It can be used to calculate the wind speeds required in a forest area for wind damage (falling trees). It is currently only suitable for researcher use. In the Säätyö project the possibility of locating the most severe wind damage areas immediately after a storm was also tested. The method is based on the spatial interpolation of wind observations. The method was used to analyze storms that caused forest damages in the summer and fall of 2020. The produced maps were considered illustrative and useful to those responsible for compiling the situational picture. The accumulation of snow on tree branches, can be modeled using weather data such as rainfall, temperature, air humidity, and wind speed. In the Säätyö project, the snow damage risk assessment model was further developed in such a way that, in addition to the accumulated snow load amount, the characteristics of the stand and the variations in terrain height were also taken into account. According to the verification performed, the importance of abiotic factors increased under extreme snow load conditions (winter 2017-2018). In ordinary winters, the importance of biotic factors was emphasized. According to the comparison, the actual snow damage could be explained well with the tested model. In the interviews and workshop, the uses of information products, their benefits, the conditions for their introduction and development opportunities were mapped. According to the results, diverse uses and benefits of information products and services were seen. Information products would make it possible to develop proactive forest management, which would reduce the economic costs caused by wind and snow damages. A more up-to-date understanding of harvesting conditions, enabled by information products, would enhance the implementation of harvesting and harvesting operations and the management of timber stocks, as well as reduce terrain, trunk and root damage. According to the study, the introduction of information is particularly affected by the availability of timeliness. Although the interviewees were not currently willing to pay for the information products developed in the project, the interviews highlighted several suggestions for the development of information products, which could make it possible to commercialize them.

1.1 Macroeconomic summary Economic recovery has consistently outperformed the technical staff’s expectations following a steep decline in activity in the second quarter of 2020. At the same time, total and core inflation rates have fallen and remain at low levels, suggesting that a significant element of the reactivation of Colombia’s economy has been related to recovery in potential GDP. This would support the technical staff’s diagnosis of weak aggregate demand and ample excess capacity. The most recently available data on 2020 growth suggests a contraction in economic activity of 6.8%, lower than estimates from January’s Monetary Policy Report (-7.2%). High-frequency indicators suggest that economic performance was significantly more dynamic than expected in January, despite mobility restrictions and quarantine measures. This has also come amid declines in total and core inflation, the latter of which was below January projections if controlling for certain relative price changes. This suggests that the unexpected strength of recent growth contains elements of demand, and that excess capacity, while significant, could be lower than previously estimated. Nevertheless, uncertainty over the measurement of excess capacity continues to be unusually high and marked both by variations in the way different economic sectors and spending components have been affected by the pandemic, and by uneven price behavior. The size of excess capacity, and in particular the evolution of the pandemic in forthcoming quarters, constitute substantial risks to the macroeconomic forecast presented in this report. Despite the unexpected strength of the recovery, the technical staff continues to project ample excess capacity that is expected to remain on the forecast horizon, alongside core inflation that will likely remain below the target. Domestic demand remains below 2019 levels amid unusually significant uncertainty over the size of excess capacity in the economy. High national unemployment (14.6% for February 2021) reflects a loose labor market, while observed total and core inflation continue to be below 2%. Inflationary pressures from the exchange rate are expected to continue to be low, with relatively little pass-through on inflation. This would be compatible with a negative output gap. Excess productive capacity and the expectation of core inflation below the 3% target on the forecast horizon provide a basis for an expansive monetary policy posture. The technical staff’s assessment of certain shocks and their expected effects on the economy, as well as the presence of several sources of uncertainty and related assumptions about their potential macroeconomic impacts, remain a feature of this report. The coronavirus pandemic, in particular, continues to affect the public health environment, and the reopening of Colombia’s economy remains incomplete. The technical staff’s assessment is that the COVID-19 shock has affected both aggregate demand and supply, but that the impact on demand has been deeper and more persistent. Given this persistence, the central forecast accounts for a gradual tightening of the output gap in the absence of new waves of contagion, and as vaccination campaigns progress. The central forecast continues to include an expected increase of total and core inflation rates in the second quarter of 2021, alongside the lapse of the temporary price relief measures put in place in 2020. Additional COVID-19 outbreaks (of uncertain duration and intensity) represent a significant risk factor that could affect these projections. Additionally, the forecast continues to include an upward trend in sovereign risk premiums, reflected by higher levels of public debt that in the wake of the pandemic are likely to persist on the forecast horizon, even in the context of a fiscal adjustment. At the same time, the projection accounts for the shortterm effects on private domestic demand from a fiscal adjustment along the lines of the one currently being proposed by the national government. This would be compatible with a gradual recovery of private domestic demand in 2022. The size and characteristics of the fiscal adjustment that is ultimately implemented, as well as the corresponding market response, represent another source of forecast uncertainty. Newly available information offers evidence of the potential for significant changes to the macroeconomic scenario, though without altering the general diagnosis described above. The most recent data on inflation, growth, fiscal policy, and international financial conditions suggests a more dynamic economy than previously expected. However, a third wave of the pandemic has delayed the re-opening of Colombia’s economy and brought with it a deceleration in economic activity. Detailed descriptions of these considerations and subsequent changes to the macroeconomic forecast are presented below. The expected annual decline in GDP (-0.3%) in the first quarter of 2021 appears to have been less pronounced than projected in January (-4.8%). Partial closures in January to address a second wave of COVID-19 appear to have had a less significant negative impact on the economy than previously estimated. This is reflected in figures related to mobility, energy demand, industry and retail sales, foreign trade, commercial transactions from selected banks, and the national statistics agency’s (DANE) economic tracking indicator (ISE). Output is now expected to have declined annually in the first quarter by 0.3%. Private consumption likely continued to recover, registering levels somewhat above those from the previous year, while public consumption likely increased significantly. While a recovery in investment in both housing and in other buildings and structures is expected, overall investment levels in this case likely continued to be low, and gross fixed capital formation is expected to continue to show significant annual declines. Imports likely recovered to again outpace exports, though both are expected to register significant annual declines. Economic activity that outpaced projections, an increase in oil prices and other export products, and an expected increase in public spending this year account for the upward revision to the 2021 growth forecast (from 4.6% with a range between 2% and 6% in January, to 6.0% with a range between 3% and 7% in April). As a result, the output gap is expected to be smaller and to tighten more rapidly than projected in the previous report, though it is still expected to remain in negative territory on the forecast horizon. Wide forecast intervals reflect the fact that the future evolution of the COVID-19 pandemic remains a significant source of uncertainty on these projections. The delay in the recovery of economic activity as a result of the resurgence of COVID-19 in the first quarter appears to have been less significant than projected in the January report. The central forecast scenario expects this improved performance to continue in 2021 alongside increased consumer and business confidence. Low real interest rates and an active credit supply would also support this dynamic, and the overall conditions would be expected to spur a recovery in consumption and investment. Increased growth in public spending and public works based on the national government’s spending plan (Plan Financiero del Gobierno) are other factors to consider. Additionally, an expected recovery in global demand and higher projected prices for oil and coffee would further contribute to improved external revenues and would favor investment, in particular in the oil sector. Given the above, the technical staff’s 2021 growth forecast has been revised upward from 4.6% in January (range from 2% to 6%) to 6.0% in April (range from 3% to 7%). These projections account for the potential for the third wave of COVID-19 to have a larger and more persistent effect on the economy than the previous wave, while also supposing that there will not be any additional significant waves of the pandemic and that mobility restrictions will be relaxed as a result. Economic growth in 2022 is expected to be 3%, with a range between 1% and 5%. This figure would be lower than projected in the January report (3.6% with a range between 2% and 6%), due to a higher base of comparison given the upward revision to expected GDP in 2021. This forecast also takes into account the likely effects on private demand of a fiscal adjustment of the size currently being proposed by the national government, and which would come into effect in 2022. Excess in productive capacity is now expected to be lower than estimated in January but continues to be significant and affected by high levels of uncertainty, as reflected in the wide forecast intervals. The possibility of new waves of the virus (of uncertain intensity and duration) represents a significant downward risk to projected GDP growth, and is signaled by the lower limits of the ranges provided in this report. Inflation (1.51%) and inflation excluding food and regulated items (0.94%) declined in March compared to December, continuing below the 3% target. The decline in inflation in this period was below projections, explained in large part by unanticipated increases in the costs of certain foods (3.92%) and regulated items (1.52%). An increase in international food and shipping prices, increased foreign demand for beef, and specific upward pressures on perishable food supplies appear to explain a lower-than-expected deceleration in the consumer price index (CPI) for foods. An unexpected increase in regulated items prices came amid unanticipated increases in international fuel prices, on some utilities rates, and for regulated education prices. The decline in annual inflation excluding food and regulated items between December and March was in line with projections from January, though this included downward pressure from a significant reduction in telecommunications rates due to the imminent entry of a new operator. When controlling for the effects of this relative price change, inflation excluding food and regulated items exceeds levels forecast in the previous report. Within this indicator of core inflation, the CPI for goods (1.05%) accelerated due to a reversion of the effects of the VAT-free day in November, which was largely accounted for in February, and possibly by the transmission of a recent depreciation of the peso on domestic prices for certain items (electric and household appliances). For their part, services prices decelerated and showed the lowest rate of annual growth (0.89%) among the large consumer baskets in the CPI. Within the services basket, the annual change in rental prices continued to decline, while those services that continue to experience the most significant restrictions on returning to normal operations (tourism, cinemas, nightlife, etc.) continued to register significant price declines. As previously mentioned, telephone rates also fell significantly due to increased competition in the market. Total inflation is expected to continue to be affected by ample excesses in productive capacity for the remainder of 2021 and 2022, though less so than projected in January. As a result, convergence to the inflation target is now expected to be somewhat faster than estimated in the previous report, assuming the absence of significant additional outbreaks of COVID-19. The technical staff’s year-end inflation projections for 2021 and 2022 have increased, suggesting figures around 3% due largely to variation in food and regulated items prices. The projection for inflation excluding food and regulated items also increased, but remains below 3%. Price relief measures on indirect taxes implemented in 2020 are expected to lapse in the second quarter of 2021, generating a one-off effect on prices and temporarily affecting inflation excluding food and regulated items. However, indexation to low levels of past inflation, weak demand, and ample excess productive capacity are expected to keep core inflation below the target, near 2.3% at the end of 2021 (previously 2.1%). The reversion in 2021 of the effects of some price relief measures on utility rates from 2020 should lead to an increase in the CPI for regulated items in the second half of this year. Annual price changes are now expected to be higher than estimated in the January report due to an increased expected path for fuel prices and unanticipated increases in regulated education prices. The projection for the CPI for foods has increased compared to the previous report, taking into account certain factors that were not anticipated in January (a less favorable agricultural cycle, increased pressure from international prices, and transport costs). Given the above, year-end annual inflation for 2021 and 2022 is now expected to be 3% and 2.8%, respectively, which would be above projections from January (2.3% and 2,7%). For its part, expected inflation based on analyst surveys suggests year-end inflation in 2021 and 2022 of 2.8% and 3.1%, respectively. There remains significant uncertainty surrounding the inflation forecasts included in this report due to several factors: 1) the evolution of the pandemic; 2) the difficulty in evaluating the size and persistence of excess productive capacity; 3) the timing and manner in which price relief measures will lapse; and 4) the future behavior of food prices. Projected 2021 growth in foreign demand (4.4% to 5.2%) and the supposed average oil price (USD 53 to USD 61 per Brent benchmark barrel) were both revised upward. An increase in long-term international interest rates has been reflected in a depreciation of the peso and could result in relatively tighter external financial conditions for emerging market economies, including Colombia. Average growth among Colombia’s trade partners was greater than expected in the fourth quarter of 2020. This, together with a sizable fiscal stimulus approved in the United States and the onset of a massive global vaccination campaign, largely explains the projected increase in foreign demand growth in 2021. The resilience of the goods market in the face of global crisis and an expected normalization in international trade are additional factors. These considerations and the expected continuation of a gradual reduction of mobility restrictions abroad suggest that Colombia’s trade partners could grow on average by 5.2% in 2021 and around 3.4% in 2022. The improved prospects for global economic growth have led to an increase in current and expected oil prices. Production interruptions due to a heavy winter, reduced inventories, and increased supply restrictions instituted by producing countries have also contributed to the increase. Meanwhile, market forecasts and recent Federal Reserve pronouncements suggest that the benchmark interest rate in the U.S. will remain stable for the next two years. Nevertheless, a significant increase in public spending in the country has fostered expectations for greater growth and inflation, as well as increased uncertainty over the moment in which a normalization of monetary policy might begin. This has been reflected in an increase in long-term interest rates. In this context, emerging market economies in the region, including Colombia, have registered increases in sovereign risk premiums and long-term domestic interest rates, and a depreciation of local currencies against the dollar. Recent outbreaks of COVID-19 in several of these economies; limits on vaccine supply and the slow pace of immunization campaigns in some countries; a significant increase in public debt; and tensions between the United States and China, among other factors, all add to a high level of uncertainty surrounding interest rate spreads, external financing conditions, and the future performance of risk premiums. The impact that this environment could have on the exchange rate and on domestic financing conditions represent risks to the macroeconomic and monetary policy forecasts. Domestic financial conditions continue to favor recovery in economic activity. The transmission of reductions to the policy interest rate on credit rates has been significant. The banking portfolio continues to recover amid circumstances that have affected both the supply and demand for loans, and in which some credit risks have materialized. Preferential and ordinary commercial interest rates have fallen to a similar degree as the benchmark interest rate. As is generally the case, this transmission has come at a slower pace for consumer credit rates, and has been further delayed in the case of mortgage rates. Commercial credit levels stabilized above pre-pandemic levels in March, following an increase resulting from significant liquidity requirements for businesses in the second quarter of 2020. The consumer credit portfolio continued to recover and has now surpassed February 2020 levels, though overall growth in the portfolio remains low. At the same time, portfolio projections and default indicators have increased, and credit establishment earnings have come down. Despite this, credit disbursements continue to recover and solvency indicators remain well above regulatory minimums. 1.2 Monetary policy decision In its meetings in March and April the BDBR left the benchmark interest rate unchanged at 1.75%.